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+\documentclass[11pt]{beamer}
+\usetheme{Madrid}
+\usepackage[utf8]{inputenc}
+\usepackage{amsmath, amssymb, amsfonts, amsthm}
+\usepackage{xcolor}
+
+\usepackage{tikz-cd}
+%\usepackage{enumitem}
+
+\author[\texttt{sebastiano.tronto@uni.lu}]{Sebastiano Tronto}
+\title{More Latex}
+\logo{\includegraphics[scale=0.1]{img/unilu.jpg}} 
+%\institute{University of Luxembourg} 
+
+\newcommand{\bs}{\textbackslash}
+
+\date{2021-03-12} 
+
+\begin{document}
+
+\begin{frame}
+  \titlepage
+\end{frame}
+
+\begin{frame}{Theorems (review)}
+  \begin{center}
+    \large
+    \texttt{\bs newtheorem\{env-name\}{\color{red}[number-with]}\{Text\}{\color{red}[number-parent]}}
+  \end{center}
+
+  \vspace{0.4cm}
+  \begin{itemize}
+    \item \texttt{env-name}: Environment name (use
+          \texttt{\bs begin\{env-name\}...})
+    \item \texttt{Text}: Theorem name to be displayed
+    \item \texttt{[number-with]} for ``shared counter''
+    \item \texttt{[number-parent]} adds x.1
+    \item {\color{red} At most one of \texttt{[number-with]}
+           and \texttt{[number-parent]}}
+  \end{itemize}
+  
+\end{frame}
+
+\begin{frame}{Theorems (review)}
+  \begin{columns}
+    \column{0.5\textwidth}
+      \includegraphics[scale=0.3]{img/thm_pre.png}
+
+      \vspace{0.2cm}
+      \vdots
+      \vspace{0.3cm}
+
+      \includegraphics[scale=0.3]{img/thm_tex.png}
+
+    \column{0.5\textwidth}
+      \includegraphics[scale=0.2]{img/thm_pdf.png}
+
+      \vspace{1cm}
+  \end{columns}
+\end{frame}
+
+
+\begin{frame}{Counters}
+  Reference: \url{https://en.wikibooks.org/wiki/LaTeX/Counters}
+
+  \vspace{0.5cm}
+  \begin{itemize}
+    \item Sections, theorems etc have an associated \emph{counter}
+
+    \vspace{0.2cm}
+    \item Common usage:
+
+          \vspace{0.1cm}
+          \texttt{\bs setcounter\{counter-name\}\{n\} \quad \%Set counter to n}
+
+          \vspace{0.1cm}
+          \texttt{\bs addtocounter\{counter-name\}\{n\}\quad\%Add n to counter}
+  \end{itemize}
+\end{frame}
+
+
+\begin{frame}{Counters}
+  
+  \begin{itemize}
+    \item Define a counter with \texttt{\bs newcounter\{name\}[number-parent]}
+
+    \vspace{0.2cm}
+    \item Change sub-numbering of defined counters:
+
+          \vspace{0.15cm}
+          \begin{center}
+            \begin{tabular}{l}
+              \texttt{\bs numberwithin\{equation\}\{section\}}
+              %\texttt{\bs numberwithout\{subsection\}\{section\}}
+            \end{tabular}
+          \end{center}
+
+    \vspace{0.2cm}
+    \item Print formatted counter with \texttt{\bs{\color{red}the}name}
+          or just number with \texttt{\bs arabic\{name\}}
+          (or \texttt{\bs alph}, \texttt{\bs Alph}, \texttt{\bs roman}, 
+          \texttt{\bs Roman}, \texttt{\bs fnsymbol})
+  \end{itemize}
+\end{frame}
+
+
+\begin{frame}{Counters}
+  
+  \begin{columns}
+    
+    \column{0.5\textwidth}
+    \begin{center}
+      {\large\textbf{Default counters}}
+  
+      \vspace{0.3cm}
+      \begin{tabular}{l}
+        %part \\
+        chapter \\
+        section \\
+        subsection \\
+        subsubsection \\
+        paragraph \\
+        %subparagraph \\
+        page \\
+        figure \\
+        %table \\
+        footnote \\
+        %mpfootnote \\
+        equation \\
+        enumi \\
+        enumii \\
+        ...
+        %enumiii \\
+        %enumiv \\
+      \end{tabular}
+    \end{center}
+
+    \column{0.5\textwidth}
+    {\large\textbf{Counter styles}}
+
+    \vspace{0.3cm}
+    \begin{tabular}{ll}
+      \texttt{arabic} & 1, 2, 3, 4... \\
+      \texttt{alph}   & a, b, c, d... \\
+      \texttt{Alph}   & A, B, C, D... \\
+      \texttt{roman}  & i, ii, iii, iv... \\
+      \texttt{Roman}  & I, II, III, IV... \\
+      \texttt{fnsymbol} & $\ast$, $\dagger$, $\ddagger$, $\S$ ...
+    \end{tabular}
+  \end{columns}
+\end{frame}
+
+\begin{frame}{Counters: change \texttt{\bs thecounter}}
+  \begin{itemize}
+    \item Change how counter is displayed by default, for example:
+
+          \vspace{0.2cm}
+          \begin{center}
+            \texttt{\bs renewcommand\{\bs thesection\}\{\bs alph\{section\}\}}
+          \end{center}
+
+    \vspace{0.3cm}
+    \item For enumerate:
+
+          \vspace{0.2cm}
+          \begin{center}
+            \begin{tabular}{l}
+              \texttt{\bs usepackage\{enumitem\}} \\
+              \texttt{\bs begin\{enumerate\}[label=\bs alph*]}
+            \end{tabular}
+          \end{center}
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{\texttt{label} and \texttt{ref}}
+  \begin{itemize}
+    \item Put \texttt{\bs label\{mark\}} immediately after the thing you want
+          to refer to (after \texttt{\bs refstepcounter\{countername\}} for
+          counters you define)
+
+    \vspace{0.3cm}
+    \item Use \texttt{\bs ref\{mark\}} or \texttt{\bs eqref\{mark\}} to refer
+          %(or \texttt{\bs eqref\{mark\}} = \texttt{(\bs ref\{mark\})})
+
+          (Pro tip: write \texttt{Proposition$\sim$\bs ref\{mark\}})
+    \vspace{0.3cm}
+    \item Compile twice!
+  \end{itemize}
+\end{frame}
+
+
+\begin{frame}{The \texttt{hyperref} package}
+  \texttt{\bs usepackage\{hyperref\}}
+
+  \vspace{1cm}
+  \begin{itemize}
+    \item Now all \texttt{\bs ref\{mark\}} become clickable!
+
+    \vspace{0.3cm}
+    \item \texttt{\bs hyperref[mark]\{text\}} for internal links
+
+    \vspace{0.3cm}
+    \item \texttt{\bs url\{www.google.com\}} or
+          \texttt{\bs href\{www.google.com\}\{Google\}} for web links
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{New commands}
+  \begin{itemize}
+    \item We have seen \texttt{\bs newcommand\{\bs command\}\{output\}}
+
+    \vspace{0.3cm}
+    \item Arguments: use \texttt{\bs newcommand\{\bs command\}[n]\{output\}}
+          and use the arguments in \texttt{output} with
+          \texttt{\#1, \#2, ... \#n} \hspace{0.4cm}(\texttt n$\leq 9$)
+
+    \vspace{0.3cm}
+    \item If \texttt{\bs command} is already defined:
+          \texttt{\bs renewcommand} (overwrite) or
+          \texttt{\bs providecommand} (use old definition, if it exists)
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{New commands - examples}
+  
+  \begin{tabular}{l|c}
+    \texttt{\bs newcommand\{hi\}\{Hello, World!\}} \\
+    \texttt{\bs hi} & Hello, world! \\
+    \\
+    \texttt{\bs newcommand\{hello\}[1]\{Hello, \#1!\}} \\
+    \texttt{\bs hello\{my friend\}} & Hello, my friend! \\
+    \\
+    \texttt{\bs renewcommand\{binom\}[2]\{bin(\#1,\#2)\}} \\
+    \texttt{\bs( \bs binom\{10\}2 \bs)} & \(bin(10,2)\)
+  \end{tabular}
+\end{frame}
+
+
+\begin{frame}{New commands - optional argument}
+  \texttt{\bs newcommand\{\bs com\}[n][default1]\{output\}}
+
+  \texttt{\bs com[first]\{other,args\}} or \texttt{\bs com\{without,first\}}
+
+  \vspace{1cm}
+  \begin{itemize}
+    \item At most one optional argument, must be \texttt{\# 1}
+
+    \vspace{0.3cm}
+    \item More complex things: use TeX primitives such as
+          \texttt{\bs ifthenelse} or see
+          \url{https://www.ctan.org/tex-archive/support/newcommand/}
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{Exercises}
+  \begin{enumerate}%[label=(\arabic*)]
+    \item Write a command \texttt{\bs mat} which takes $4$ arguments and
+          outputs a $2\times 2$ matrix with those arguments as entries
+          (use \texttt{pmatrix}).
+
+    \vspace{0.5cm}
+    \item Write a command to define a function case-by-case ($2$ cases,
+          $4$ arguments). Use the \texttt{cases} environment:
+
+          \vspace{0.2cm}
+          \begin{columns}
+            \column{0.45\textwidth}
+            \begin{center}\begin{tabular}{l}
+              \texttt{\bs begin\{cases\}} \\
+              \texttt{\quad 1 \& 2 \bs\bs \quad3 \& 4} \\
+              \texttt{\bs end\{cases\}}
+            \end{tabular}\end{center}
+
+            \column{0.09\textwidth}
+              \begin{center} $\implies$ \end{center}
+
+            \column{0.45\textwidth}
+            \begin{align*}
+              \begin{cases} 1 & 2 \\ 3 & 4 \end{cases}
+            \end{align*}
+          \end{columns}
+  \end{enumerate}
+\end{frame}
+
+
+\begin{frame}{Pictures}
+  \texttt{\bs usepackage\{graphicx\}} 
+
+  \texttt{\bs includegraphics[options]\{picture.jpg\}} 
+
+  \vspace{1cm}
+  Options (comma-separated) include:
+
+  \vspace{0.2cm}
+  \begin{itemize}
+    \item \texttt{scale=x} (scale by a factor of x)
+    \item \texttt{width=x} and \texttt{height=y} (if both specified picture
+          is distorted)
+    \item \texttt{angle=$\alpha$} (rotate)
+  \end{itemize}
+\end{frame}
+
+
+\begin{frame}{Figures}
+  \texttt{\bs begin\{figure\}[place]}
+  
+  \vspace{1cm}
+  \begin{itemize}
+    \item Figure outside normal text flow.
+    \item \texttt{place}: \texttt{h} (here), \texttt{t} (top) or \texttt{b}
+          (bottom).
+    \item Can add \emph{caption}
+  \end{itemize}
+
+  \vspace{0.3cm}
+  \begin{center} \begin{tabular}{l}
+    \texttt{\bs begin\{figure\}[h]} \\
+    \texttt{\qquad\bs centering \qquad \% recommended} \\
+    \texttt{\qquad \bs includegraphics\{picture.jpg\}} \\
+    \texttt{\qquad \bs caption\{Description of the picture\}} \\
+    \texttt{\bs end\{figure\}}
+  \end{tabular} \end{center}
+\end{frame}
+
+
+\begin{frame}{Wrapping text around figures}
+
+ \texttt{\bs usepackage\{{\color{red}wrapfig}\}}
+
+  \texttt{\bs begin\{wrapfigure\}{\color{red}\{alignment\}\{width\}}}
+  
+  \vspace{1cm}
+  \begin{itemize}
+    \item \texttt{alignment}: \texttt{l} (left) or \texttt{r} (right)
+    \item Must specify \texttt{width}
+    \item Works the same as \texttt{figure}
+  \end{itemize}
+
+  \vspace{0.3cm}
+  \begin{center} \begin{tabular}{l}
+    \texttt{\bs begin\{wrapfigure\}{\color{red}\{l\}\{0.5\bs textwidth\}}} \\
+    \texttt{\qquad\bs centering} \\
+    \texttt{\qquad \bs includegraphics\{picture.jpg\}} \\
+    \texttt{\qquad \bs caption\{Description of the picture\}} \\
+    \texttt{\bs end\{wrapfigure\}}
+  \end{tabular} \end{center}
+\end{frame}
+
+
+\begin{frame}{Lengths}
+  Reference: \url{https://en.wikibooks.org/wiki/LaTeX/Lengths}
+
+  \vspace{0.5cm}
+  \begin{itemize}
+    \item Similar to counters:
+
+          \vspace{0.3cm}
+          \begin{center}\begin{tabular}{l}
+            \texttt{\bs newlength\{\bs lengthname\}}\\
+            \texttt{\bs setlength\{\bs lengthname\}\{value\}}
+          \end{tabular}\end{center}
+          
+    \vspace{0.3cm}
+    \item \texttt{value}: number followed by unit
+          (\texttt{12pt}, \texttt{1.2cm}, \texttt{65mm}, \dots)
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{Lengths}
+  Default lengths:
+
+  \vspace{0.5cm}
+  \begin{itemize}
+    \item \texttt{\bs textwidth}: width of text in a page
+    \item \texttt{\bs textheight}: height of text in a page
+    \item \texttt{\bs baselineskip}: space between lines in same paragraph
+    \item \texttt{\bs parskip}: space between paragraphs
+    \item \texttt{\bs parindent}: indentation of first line of a paragraph
+    \item \dots
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{Manual spacing}
+  \begin{itemize}
+    \item \texttt{\bs vspace\{length\}} and \texttt{\bs hspace\{length\}}
+
+    \vspace{0.2cm}
+    \item Fill space: \texttt{\bs vfill} and \texttt{\bs hfill}
+
+    \vspace{0.2cm}
+    \item Fill line with ``decoration'':
+          \texttt{\bs hrulefill} and \texttt{\bs dotfill}
+
+    \vspace{0.2cm}
+    \item Example:
+    
+          \vspace{0.2cm}
+          \begin{center}
+          \texttt{First name: \bs hrulefill \bs quad Last name: \bs hrulefill}
+          \end{center}
+  \end{itemize}
+\end{frame}
+
+
+
+\begin{frame}{Bibliography}
+  Simple bibliography with \texttt{thebibliography} environment:
+
+  \vspace{0.5cm}
+  \begin{center}\begin{tabular}{l}
+    \texttt{\bs begin\{thebibliography\}\{99\}} \\
+    \texttt{\qquad\bs bibitem\{knuth68\}} \\
+    \texttt{\qquad\qquad Donald Knuth, The Art of Computer Programming,} \\
+    \texttt{\qquad\qquad Volume I, 1968, Addison-Wesley}\\
+    \texttt{\bs end\{thebibliography\}}
+  \end{tabular}\end{center}
+
+  %\vspace{0.5cm}
+  %And cite with \texttt{\bs cite\{knuth68\}}
+\end{frame}
+
+
+\begin{frame}{Bibligraphy}
+  \begin{itemize}
+    \item Simple citation: \texttt{\bs cite\{knuth68\}}
+
+    \vspace{0.3cm}
+    \item Cite multiple sources: \texttt{\bs cite\{source1, source2\}}
+
+    \vspace{0.3cm}
+    \item Cite specific part with \texttt{\bs cite[p.$\sim$42]\{source\}}
+  \end{itemize}
+\end{frame}
+
+
+\begin{frame}{Bibliography: BibTeX}
+  \begin{itemize}
+    \item Separate file \texttt{mybib.bib}, different syntax:
+
+          \begin{center}\begin{tabular}{l}
+            \texttt{@book\{knuth68,} \\
+            \texttt{\qquad author    = "Donald Knuth",}\\
+            \texttt{\qquad title     = "The Art of Computer Programming",}\\
+            \texttt{\qquad publisher = "Addison-Wesley",}\\
+            \texttt{\qquad volume    = "I",}\\
+            \texttt{\qquad year      = "1968",} \\
+            \texttt{\}}
+          \end{tabular}\end{center}
+
+    \vspace{0.3cm}
+    \item Include bibliography in your \texttt{.tex} file:
+
+          \begin{center}\begin{tabular}{l}
+            \texttt{\bs bibliographystyle\{plain\}}\\
+            \texttt{\bs bibliography\{mybib\}}
+          \end{tabular}\end{center}
+  \end{itemize}
+\end{frame}
+
+
+\begin{frame}{Bibliography: BibTeX}
+  \begin{itemize}
+    \item Compile, generate bibliography, compile, compile
+
+    \vspace{0.3cm}
+    \item Books in \texttt{.bib} file but not cited do not appear
+
+    \vspace{0.3cm}
+    \item Citing articles and other: see \url{https://en.wikibooks.org/wiki/%
+          LaTeX/Bibliography\_Management\#Standard\_templates}
+
+    \vspace{0.3cm}
+    \item Find BibTeX citations on \url{https://scholar.google.com}
+  \end{itemize}
+\end{frame}
+
+\end{document}
+