  These lectures notes were written for a summer school on Mathematics for
post-quantum cryptography in Thi\`es, Senegal. They try to provide a guide for
Masters' students to get through the vast literature on elliptic curves,
without getting lost on their way to learning isogeny based cryptography. They
are by no means a reference text on the theory of elliptic curves, nor on
cryptography; students are encouraged to complement these notes with some of
the books recommended in the bibliography.
  The presentation is divided in three parts, roughly corresponding to the
three lectures given. In an effort to keep the reader interested, each part
alternates between the fundamental theory of elliptic curves, and applications
in cryptography. We often prefer to have the main ideas flow smoothly, rather
than having a rigorous presentation as one would have in a more classical book.
The reader will excuse us for the inaccuracies and the omissions.
