# Isogeny Graphs in Cryptography These lectures notes were written for the summer school on *Graph Theory Meets Cryptography* in Würzburg, Germany, in July 2019. Their goal is to survey the mathematical background of isogeny-based cryptography, a blossoming new field with applications to post-quantum cryptography and blockchains. They are by no means a reference text on the theory of elliptic curves, nor on cryptography; readers are encouraged to complement these notes with the references given in the bibliography.