This document gives a synthetic overview of my research since 2006. It is focused on algorithms for asymmetric (public-key) cryptography—especially, though not exclusively, Elliptic Curve Cryptography; its generalizations including Hyperelliptic Curve Cryptography; and its derivatives including Isogeny-Based Cryptography, one of the newer branches of post-quantum cryptography. We also consider the implementation of post-quantum cryptosystems in a broader sense. The contributions range from theoretical and mathematical foundations through to low-level implementation techniques.