  The aim of these notes is to provide an introduction to Anti-de Sitter
geometry, with special emphasis on dimension three and on the relations with
Teichm\"uller theory, whose study has been initiated by the seminal paper of
Geoffrey Mess in 1990. In the first part we give a broad introduction to
Anti-de Sitter geometry in any dimension. The main results of Mess, including
the classification of maximal globally hyperbolic Cauchy compact manifolds and
the construction of the Gauss map, are treated in the second part. Finally, the
third part contains related results which have been developed after the work of
Mess, with the aim of giving an overview on the state-of-the-art.
