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diff --git a/src/blog/2024-12-26-taming-cpp-raii/taming-cpp-raii.md b/src/blog/2024-12-26-taming-cpp-raii/taming-cpp-raii.md
index 88744bb..f35596f 100644
--- a/src/blog/2024-12-26-taming-cpp-raii/taming-cpp-raii.md
+++ b/src/blog/2024-12-26-taming-cpp-raii/taming-cpp-raii.md
@@ -278,3 +278,5 @@ other object-oriented languages like Java or C#.  C++ gives you a lot
 of control over the low-level details, and some powerful tools to make
 use of it, in exchange for a lot of complexity that you must, at the
 very least, be aware of.
+
+*Next in the series: [RAII](../2025-01-21-taming-cpp-templates)*
diff --git a/src/blog/2025-01-21-taming-cpp-templates/taming-cpp-templates.md b/src/blog/2025-01-21-taming-cpp-templates/taming-cpp-templates.md
new file mode 100644
index 0000000..fe1ca5d
--- /dev/null
+++ b/src/blog/2025-01-21-taming-cpp-templates/taming-cpp-templates.md
@@ -0,0 +1,578 @@
+# Taming C++, episode 3: templates, constraints and concepts
+
+*This post is part of a [series](../../series)*
+
+If you have ever written some C++, you have probably already used
+[templates](https://en.cppreference.com/w/cpp/language/templates).
+For example, you may have done something like this:
+
+```
+std::vector<int> v {1, 2, 3};
+v[1] = -1;
+std::cout << v[0] << ", " << v[1] << ", " << v[2] << std::endl;
+```
+
+The type
+[`std::vector<int>`](https://en.cppreference.com/w/cpp/container/vector)
+is the *specialization* of the *class template* `std::vector`. If you
+wanted a vector of chars, for example, you could do something like this:
+
+```
+std::vector<char> w {'a', '!', '\n' };
+```
+
+Oversimplifying a bit, a template in C++ is a type (or a
+[function](https://en.cppreference.com/w/cpp/language/function_template))
+that depends on some other type or constant. They are quite powerful,
+because they do a lot of work at compile time, so you can write generic
+code without impacting performance. But at the same time they can be
+quite intimidating, because as soon as you get something wrong around
+templates the compiler will throw hundreds of lines of unreadable
+error messages at you.
+
+In this post I'll briefly explain what templates are and how to
+write simple class and function templates. After that, I am going to
+work through a little piece of code I wrote, starting from a simple
+implementation and working out a general "templatized" version
+step by step. I am going to use C++20 so that I can make use of
+[concepts](https://en.cppreference.com/w/cpp/language/constraints),
+so make sure to compile with `-std=c++20` if you are compiling with a
+current version of GCC or Clang - in the future it may not be necessary
+anymore, but currently both major compilers default to C++17.
+
+You can find the code examples for this post in the
+[companion repository for this series](https://git.tronto.net/taming-cpp),
+and if you want you can also have a look at the final version
+of my tiny library
+[on my git page](https://git.tronto.net/zmodn/file/README.md.html). For
+this post I am going to use Clang as a compiler, because I find its
+error messages more readable most of the times.
+
+## Templates
+
+The first thing one must understand about templates is that **a
+[class template](https://en.cppreference.com/w/cpp/language/class_template)
+is not a class, it is a template for a class**.  Similarly, a function
+template is not a function, it is a template for a function.
+
+This means that a class template must be *specialized* to become an
+actual class. The compiler won't generate any code for templates that
+are not used anywhere. In other words, a template becomes something
+concrete only when you provide concrete template arguments.
+
+Different specializations of the same template are different types: one
+cannot, for example, assign an `std::vector<int>` object to an
+`std::vector<double>` variable.
+
+### Class templates
+
+As an example, let's take a simple standard library class such as
+[`std::pair`](https://en.cppreference.com/w/cpp/utility/pair).
+It could be implemented as follows (see
+[pair.cpp](https://git.tronto.net/taming-cpp/file/templates/pair.cpp.html)):
+
+```
+template<typename S, typename T>
+class Pair {
+public:
+        S first;
+        T second;
+
+        Pair(S s, T t) : first{s}, second{t} {}
+
+        void print() const { // Kinda useless, but I need it to explain a thing
+                std::cout << "(" << first << ", " << second << ")";
+        }
+};
+```
+
+And then you can declare variables of type `Pair` - or rather, of a
+specialization of `Pair`:
+
+```
+Pair<int, char> p(42, 'x');
+```
+
+The compiler can also deduce the template argument types for you, so
+the statement above is equivalent to
+
+```
+Pair p(42, 'x');
+```
+
+So using templates is not that hard. Nice!
+
+### Splitting declaration and implementation
+
+Let's say you want to make our example class template `Pair` a bit cleaner
+by splitting the declaration and the implementation of the `print()`
+function. To do so, we have to re-declare the template parameters:
+
+```
+template<typename S, typename T>
+class Pair {
+public:
+        S first;
+        T second;
+
+        Pair(S s, T t) : first{s}, second{t} {}
+
+        void print() const;
+};
+
+template<typename S, typename T>
+void Pair<S, T>::print() const {
+        std::cout << "(" << first << ", " << second << ")";
+}
+```
+
+The syntax is not amazing, but it can be worth it for longer functions.
+
+### Function templates
+
+Templates are not limited to classes, we can also have function templates.
+A classic example is a
+[swap](https://en.cppreference.com/w/cpp/algorithm/swap) function, which
+can be implemented like this:
+
+```
+template<typename T>
+void swap(T& a, T& b) {
+        T tmp = a;
+        a = b;
+        b = tmp;
+}
+```
+
+(Here I am using
+[references](https://en.cppreference.com/w/cpp/language/reference),
+which in case you don't know are just a simplified syntax for pointers.)
+
+Let's take this simple example to show an important property of templates.
+Let's say that, perhaps by mistake, we implemented the swap function
+using different template types for `a` and `b` (see
+[swap.cpp](https://git.tronto.net/taming-cpp/file/templates/swap.cpp.html)):
+
+```
+template<typename S, typename T>
+void swap(S& a, T& b) {
+        S tmp = a;
+        a = b;
+        b = tmp;
+}
+```
+
+This is actually ok, because **templates are not type-checked until
+they are specialized**. And in fact we may legitimately want to
+swap variables of different types, for example:
+
+```
+int x = 3;
+double y = 1.0;
+swap(x, y);
+```
+
+The code above will compile just fine, because C++ accepts implicit type
+conversions between `int` and `double`. However, this:
+
+```
+int x = 3;
+std::string y = "1.0";
+swap(x, y);
+```
+
+Will not compile:
+
+```
+swap.cpp:6:6: error: assigning to 'int' from incompatible type 'std::basic_string<char>'
+    6 |         a = b;
+      |             ^
+swap.cpp:13:2: note: in instantiation of function template specialization 'swap<int, std::basic_string<char>>' requested here
+   13 |         swap(x, y);
+      |         ^
+1 error generated.
+```
+
+The error messages we get when misusing templates are not always nice
+and readable as this one, they can literaly be hundreds of lines long.
+Luckily, C++20 introduced
+[constraints and concepts](https://en.cppreference.com/w/cpp/language/constraints)
+to make these error messages more meaningful - we'll see some examples below.
+
+### Non-type parameters
+
+Objects, not just types, can be template parameters. A classic example
+is [`std::array`](https://en.cppreference.com/w/cpp/container/array),
+a fixed-size container where the capacity is fixed at compile time (see
+[std_array.cpp](https://git.tronto.net/taming-cpp/file/templates/std_array.cpp.html)
+for an example).
+
+Non-type parameters can be constants of any *structural type* - see
+[this page](https://en.cppreference.com/w/cpp/language/template_parameters)
+for a precise definition. Remember that you can only specialize them
+with compile-time (i.e. `constexpr`) constants!
+
+With non-type parameter you can do pretty wild stuff, see for example
+[factorial.cpp](https://git.tronto.net/taming-cpp/file/templates/factorial.cpp.html)
+- although this specific example is not very useful, since it can easily
+be replaced by a constexpr function.
+
+Fun fact: if you use `auto`, you don't even have to specify a type for
+a non-type parameter. For example, the following code works just fine (see
+[println.cpp](https://git.tronto.net/taming-cpp/file/templates/println.cpp.html)):
+
+```
+#include <iostream>
+
+template<auto X> void println() { std::cout << X << std::endl; }
+
+int main() {
+        println<1.23>();
+        println<42>();
+
+        return 0;
+}
+```
+
+Later we'll see a more useful application of this.
+
+### Default values
+
+Template parameters can have default value, for example:
+
+```
+template<typename S = int, typename T = S>
+class Pair {
+public:
+        S first;
+        T second;
+
+        // And so on...
+```
+
+With the code above, `Pair` is going to denote a pair of two integers,
+and `Pair<double>` is going to denote a pair of two doubles.
+
+Non-type parameters can have default values too:
+
+```
+template<typename T, int N = 10>
+class MyArray {
+        // A container with 10 elements by default
+};
+```
+
+### Variadic templates
+
+Like with functions, templates can have a variable number of parameters.
+A classic example is
+[`std::tuple`](https://en.cppreference.com/w/cpp/utility/tuple), which
+works similarly to `std::pair`, but accepts any number of items.
+
+## Contraints and concepts
+
+To explain the last features I want to talk about, I am going to use a
+simlpe, albeit slightly unusual, example: let's implement a class
+template for
+[the integers modulo `N`](https://en.wikipedia.org/wiki/Modular_arithmetic),
+where `N` is a fixed at compile-time.
+
+We may start with something like this (see
+[zmodn-1.cpp](https://git.tronto.net/taming-cpp/file/templates/zmodn-1.cpp.html)):
+
+```
+#include <iostream>
+#include <optional>
+#include <tuple>
+
+std::tuple<int, int, int> extended_gcd(int a, int b) {
+        if (b == 0) return {a, 1, 0};
+        auto [g, x, y] = extended_gcd(b, a%b);
+        return {g, y, x - y*(a/b)};
+}
+
+template<int N>
+class Zmod {
+public:
+        int value;
+
+        Zmod(int z) : value{(z%N + N) % N} {}
+
+        Zmod operator+(const Zmod& z) const { return value + z.value; }
+        Zmod operator-(const Zmod& z) const { return value - z.value; }
+        Zmod operator*(const Zmod& z) const { return value * z.value; }
+
+        std::optional<Zmod> inverse() const {
+                auto [g, a, _] = extended_gcd(value, N);
+                return g == 1 ? Zmod(a) : std::optional<Zmod>{};
+        }
+
+        std::optional<Zmod> operator/(const Zmod& d) const {
+                auto i = d.inverse();
+                return i ? (*this) * i.value() : i;
+        }
+
+        std::optional<Zmod> operator/=(const Zmod& d) {
+                auto q = *this / d;
+                return q ? (*this = q.value()) : q;
+        }
+};
+
+int main() {
+        Zmod<57> x(34);
+        Zmod<57> y(11);
+
+        std::cout << "34 * 11 = " << (x * y).value << " (mod 57)" << std::endl;
+
+        if (auto inv = y.inverse(); inv)
+                std::cout << "11 * " << inv.value().value << " = 1 (mod 57)" << std::endl;
+        else
+                std::cout << "11 is not invertible in Z/57Z" << std::endl;
+
+        return 0;
+}
+```
+
+So we are just using a single non-type template parameter, no big deal.
+
+But now let's say that by accident I type something like:
+
+```
+int main() {
+        Zmod<0> z(13); // Oops, I meant Zmod<10>
+}
+```
+
+Unfortunately, this code is going to compile just fine, and I'll get
+a horrible run-time error. It would be cool if there was some way
+to *constrain* the template argument to only allow positive integers.
+Which brings us to...
+
+### Constraints
+
+[Constraints](https://en.cppreference.com/w/cpp/language/constraints)
+are a way to prevent nasty run-time errors and / or make compiler errors
+more meaningful when using templates; they were added in C++20.
+
+In our case, introducing our constraint is quite simple (see
+[zmodn-2.cpp](https://git.tronto.net/taming-cpp/file/templates/zmodn-2.cpp.html)):
+
+```
+template<int N>
+requires (N > 1)
+class Zmod {
+        // Same as before...
+};
+```
+
+And now if we try to compile the `Zmod<0>` declaration we get:
+
+```
+zmodn-2.cpp:51:2: error: constraints not satisfied for class template 'Zmod' [with N = 0]
+   51 |         Zmod<0> z(157);
+      |         ^~~~~~~
+zmodn-2.cpp:12:11: note: because '0 > 1' (0 > 1) evaluated to false
+   12 | requires (N > 1)
+      |           ^
+1 error generated.
+```
+
+Nice!
+
+### Making it more generic
+
+For one specific application of this class, which I may write about in
+a future post, I need `N` to be very larger, larger than a 32-bit
+integer. So I should probably change `int` to `long long` or `int64_t`.
+Except I would like to work with numbers that are even larger than 64
+bits!  This means I should find (or write) a library for large integers,
+but at the same time I want to keep the `Zmod` class independent of a
+specific library... I should definitely make `Zmod` parametric in the
+type of N.
+
+In order to do so, I can use a non-type parameter declared `auto` and
+[`decltype()`](https://en.cppreference.com/w/cpp/language/decltype) (see
+[zmodn-3.cpp](https://git.tronto.net/taming-cpp/file/templates/zmodn-3.cpp.html)):
+
+```
+template<auto N>
+requires (N > 1)
+class Zmod {
+public:
+        decltype(N) value;
+
+        Zmod(decltype(N) z) : value{(z%N + N) % N} {}
+
+        // The rest is unchanged
+};
+```
+
+And of course I should also templatize the `extended_gcd()` function -
+you can see the full code in
+[zmodn-3.cpp](https://git.tronto.net/taming-cpp/file/templates/zmodn-3.cpp.html).
+
+Now we can use any type as a "base" for our modular integer! Well, almost.
+I mentioned above that the type we use must be *structural*, but that is
+relatively easy to satisfy. A bigger problem is that our type must
+allow for compile-time constants - so we need, at least, a `constexpr`
+constructor. I could not find a suitable library online, so I ended
+up writing my own - see
+[bigint.h](https://git.tronto.net/taming-cpp/file/templates/bigint.h.html).
+
+The code is simple and not very efficient, but this library is not meant
+to be efficient. I am just using it for educational purposes.
+
+To show it off, we can do stuff like this:
+
+```
+int main() {
+        constexpr BigInt N("1000000000000000000000000000000");
+        Zmod<N> x(BigInt("123456781234567812345678"));
+        Zmod<N> y(BigInt("987654321987654321"));
+
+        std::cout << x.value << " * "
+                  << y.value << " (mod " << N << ") = "
+                  << (x * y).value << std::endl;
+
+        // Prints:
+        // 123456781234567812345678 * 987654321987654321 (mod 1000000000000000000000000000000) = 5237873798636805364022374638
+
+        return 0;
+}
+```
+
+But now we have once again a constraint problem. We could for example write
+
+```
+        constexpr double M = 3.14;
+        Zmod<M> z(M);
+```
+
+And sure, this will fail with an understandable error message related to
+the modulo operation `%`, but it is not hard to imagine that in other
+situations this could be a problem. So we should put a constraint on
+our type, in this case `decltype(N)`.
+
+At first I achieved this using the *type trait*
+[`std::is_integral`](https://en.cppreference.com/w/cpp/types/is_integral):
+
+```
+template<auto N>
+requires (N > 1) && std::is_integral<decltype(N)>::value
+class Zmod {
+        // Etc...
+};
+```
+
+Type traits are defined in the `<type_traits>` header. For an overview
+check out this nice
+[blog post](https://www.internalpointers.com/post/quick-primer-type-traits-modern-cpp).
+
+Unfortunately, my custom big integer class does not satisfy
+`std::is_integral`.  So I have to define my own set of constraints.
+
+### Concepts
+
+Along with constraints, C++20 also introduced the possibility to define
+and name a custom set of requirements. This can be done with *concepts*.
+In our example, we can require that our type supports all the operations
+we need (see
+[zmodn-4.cpp](https://git.tronto.net/taming-cpp/file/templates/zmodn-4.cpp.html)):
+
+```
+template<typename T>
+concept Integer = requires(T a, T b, int i) {
+        {T(i)};
+
+        {a + b} -> std::same_as<T>;
+        {a - b} -> std::same_as<T>;
+        {a * b} -> std::same_as<T>;
+        {a / b} -> std::same_as<T>;
+        {a % b} -> std::same_as<T>;
+
+        {a == b} -> std::same_as<bool>;
+        {a != b} -> std::same_as<bool>;
+};
+```
+
+Let's break this down. The first line introduces a template, because our
+concept depends on a type parameter `T`. The second line introduces the
+definition of the concept: the arguments to the `requires` keyword are
+variables that we are going to use in our concept definition.
+
+The third line is where things get interesting. The notation `{T(i)}`
+means "`T(i)` must be a valid expression", where `i` is any variable of
+type `int`, as defined in the `requires` arguments. In other words, we
+are asking that type `T` has a constructor that takes a single integer
+parameter.
+
+The other lines are all similar, and they expand on this concept.
+For example `{a % b} -> std::same_as<T>` requires that the operator `%` is
+defined between variables of type T; moreover, the `-> std::same_as<T>`
+notation declares that we want the resulting type to satisfy the
+type trait `std::same_as<T>` - in other words, we are asking for
+`T operator%(T)` to be defined as a member function of `T`.
+
+Note that we are not requiring anything about what these operations
+actually do: we are only requiring that they are defined. If for some
+reason a custom floating point type defines an operator `%` and all other
+arithmetic operations that we require, it could be used for our `zmod<N>`
+class without any complaints from the compiler, but the results may not
+be what we expect.
+
+We can use our newly-defined concept in two ways. As part of a requires
+clause:
+
+```
+template<typename T>
+requires Integer<T>
+std::tuple<T, T, T> extended_gcd(T a, T b) { /* Same as before */ }
+
+template<auto N>
+requires (N > 1) && Integer<decltype(N)>
+class Zmod { /* Same as before */ }
+```
+
+Or with the following syntax sugar:
+
+```
+template<Integer T>
+std::tuple<T, T, T> extended_gcd(T a, T b) { /* Same as before */ }
+
+template<Integer auto N>
+requires(N > 1)
+class Zmod { /* Same as before */ }
+```
+
+I tend to prefer the second way because it is more compact and it reads
+nicely: in the first of the two templates, we declare `T` as if it were
+a variable of type `Integer`.
+
+And now if we try to compile `Zmod<3.14>` the compiler gives us a clear
+error message:
+
+```
+zmodn-4.cpp:68:3: error: constraints not satisfied for class template 'Zmod' [with N = 3.140000e+00]
+   68 |          Zmod<M> z(4);
+      |          ^~~~~~~
+zmodn-4.cpp:29:10: note: because 'decltype(3.1400000000000001)' (aka 'double') does not satisfy 'Integer'
+   29 | template<Integer auto N>
+      |          ^
+zmodn-4.cpp:16:5: note: because 'a % b' would be invalid: invalid operands to binary expression ('double' and 'double')
+   16 |         {a % b} -> std::same_as<T>;
+      |            ^
+1 error generated.
+```
+
+## Conclusion
+
+Templates are a very powerful tool that allow creating zero-cost
+abstractions (if you don't count the longer compile time as a cost).
+With the addition of constraints and concepts in C++20 it became easier to
+define requirements on the template parameters and catch template misuse
+at compile time.
+
+In some way concepts offer a new style of abstraction, similar in scope
+to object-oriented programming. Since I am not a fan of OOP, I like that
+we have this new option, and I am going to play around with whenever I
+get the chance.
diff --git a/src/series/series.md b/src/series/series.md
index 84bdad0..afbf3dd 100644
--- a/src/series/series.md
+++ b/src/series/series.md
@@ -49,3 +49,4 @@ My adventures in learning C++ as a C programmer.
 
 * Episode 1: [motivation](../blog/2024-04-30-taming-cpp-motivation)
 * Episode 2: [RAII](../blog/2024-12-26-taming-cpp-raii)
+* Episode 3: [templates, constraints and concepts](../blog/2025-01-21-taming-cpp-templates)