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+\documentclass[11pt]{beamer}
+\usetheme{Madrid}
+\usepackage[utf8]{inputenc}
+\usepackage{amsmath, amssymb, amsfonts, amsthm}
+\usepackage{xcolor}
+
+\usepackage{tikz-cd}
+
+\author[\texttt{sebastiano.tronto@uni.lu}]{Sebastiano Tronto}
+\title{Presentations in LaTeX with Beamer}
+\logo{\includegraphics[scale=0.1]{img/unilu.jpg}} 
+%\institute{University of Luxembourg} 
+
+\newcommand{\bs}{\textbackslash}
+
+\date{2021-03-26} 
+
+\begin{document}
+
+\begin{frame}
+  \titlepage
+\end{frame}
+
+\begin{frame}{Why presentation with LaTeX?}
+  Pros:
+
+  \vspace{0.2cm}
+  \begin{itemize}
+    \item Easy to include formulas and theorems
+    \item Portability: \texttt{pdf} = \textbf{portable} document format
+    \item Very fast to get ``good enough'' results (subjective)
+  \end{itemize}
+
+  \vspace{0.5cm}
+  Cons:
+
+  \vspace{0.2cm}
+  \begin{itemize}
+    \item Advanced animations not possible with pdf
+    \item Lack of other presentation-specific features
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{Structure of a Beamer document}
+  \includegraphics[scale=0.35]{img/beamer.png}
+\end{frame}
+
+\begin{frame}{The \texttt{frame} environment}
+  \texttt{\bs begin\{frame\}[options]\{Title\} \,\dots\, \bs end\{frame\}}
+
+  \vspace{0.5cm}
+  Useful options:
+  \begin{itemize}
+    \item \texttt{plain}: no bars on bottom or side
+    \item \texttt{shrink}: content is shrunk to fit in the slide
+    \item \texttt{fragile}: when you have \texttt{tikzpicture},
+          \texttt{listings} or similar 
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{Basic animations}
+  \begin{itemize}
+    \item \texttt{\bs pause} for a simple break
+
+    \vspace{0.3cm}
+    \item \texttt{\bs only<start-(end)>\{\emph{stuff}\}} to show
+          \emph{\texttt{stuff}} only on some slides
+          
+          Shortcut for lists: \texttt{\bs item<\dots>} or
+          \texttt{\bs begin\{itemize\}[<+->]}
+
+    \vspace{0.3cm}
+    \item Optional:
+          \texttt{\bs setbeamercovered\{transparent\}} (see end of slides)
+
+    \vspace{0.3cm}
+    \item \texttt{\bs uncover<\dots>} does not take space when invisible
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{Theorems and lists}
+  \begin{theorem} This is a Theorem \end{theorem}
+  \begin{proof} With proof \end{proof}
+  
+  \begin{itemize}
+    \item \texttt{theorem}, \texttt{proof} and \texttt{definition} already
+          included with beamer.
+    \item Define new theorems as usual (they get a box automatically)
+  \end{itemize}
+\end{frame}
+
+\begin{frame}[fragile]{Custom blocks}
+
+  {
+    \setbeamercolor{block title}{fg=blue,bg=green}
+    \setbeamercolor{block body}{fg=black,bg=pink!50}
+    \begin{block}{A custom block, with ugly colors}
+      \begin{verbatim}
+{
+    \setbeamercolor{block title}{fg=blue,bg=green}
+    \setbeamercolor{block body}{fg=black,bg=pink!50}
+    
+    \begin{block}{A custom block, with ugly colors}
+        ...
+    \end{block}
+}
+      \end{verbatim}
+    \end{block}
+  }
+\end{frame}
+
+
+\begin{frame}{Multiple columns}
+  \begin{columns}
+  \column{0.3\textwidth}
+    \texttt{\bs begin\{columns\}}
+
+    \texttt{\qquad\bs column\{\emph{width}\}}
+
+    \texttt{\qquad(stuff)}
+
+    \texttt{\qquad\bs column\{\emph{width}\}}
+
+    \texttt{\qquad(more stuff)}
+
+    \texttt{\qquad\qquad\vdots}
+
+    \texttt{\bs end\{columns\}}
+  \column{0.7\textwidth}
+    \begin{itemize}
+      \item \texttt{\emph{width}} is a length (example:
+            \texttt{0.7\bs textwidth})
+      \item Example: picture on the left, text on the right
+      \item Not specific to Beamer
+      \item Alternative: \texttt{tabular}
+    \end{itemize}
+  \end{columns}
+
+\end{frame}
+
+\begin{frame}{Some advice}
+  \begin{itemize}
+    \item Do not prepare too many slides (1-2 minutes per slide)
+    \item Do not write too much in each slide (split if necessary)
+    \item Pictures and \texttt{itemize}s are great, sentences are not
+    \item Animations are ok (but are they worth the effort?)
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{Examples}
+  Three examples will follow:
+  \begin{itemize}
+    \item A horrible slide
+    \item A better slide with the same content
+    \item A better better slide that took a little more time to write
+  \end{itemize}
+\end{frame}
+
+\begin{frame}{Diophantine equations (bad)}
+  Diophantine equations are a very old problem, dating back to Diophantus of
+  Alexandria (III century A.D.).
+
+  Despite this, they are still today a very hard problem, and there is
+  no general method or algorithm to solve them.
+
+  A notable example is \emph{Fermat's Last Theorem}, stated for the first time
+  in 1637 but proved to be true only in 1995, after more than 350 years!
+\end{frame}
+
+
+\begin{frame}{Diophantine Equations (better)}
+  \begin{itemize}
+    \item Very old problem
+    
+    \vspace{0.3cm}
+    \item Very simple formulation, but very hard to solve!
+    
+    \vspace{0.3cm}
+    \item ``Fermat's Last Theorem'': stated in 1637 - proved in 1995
+  \end{itemize}
+\end{frame}
+
+\setbeamercovered{transparent}
+\begin{frame}{Diophantine Equations (better better)}
+  \begin{columns}
+  \column{0.45\textwidth}
+    \begin{figure}
+      \begin{center}
+        \includegraphics[scale=0.2]{img/diophantus.jpg}
+        {\footnotesize Diophantus of Alexandria\\ (III century A.D.)}
+      \end{center}
+    \end{figure}
+  \column{0.55\textwidth}
+    \begin{itemize}
+      \item<1-> Very old problem
+      \item<2-> Very simple formulation, but very hard to solve!
+      \item<3-> \emph{Fermat's Last Theorem}: stated in 1637 - proved in 1995
+    \end{itemize}
+  \end{columns}
+\end{frame}
+
+
+\end{document}