Contributors in mathematics, computer science, and engineering introduce students and other professionals in any of their fields to the theory and algorithms involved in elliptic and hyper-elliptic curve cryptology in great detail. The text contains very few proofs, but provides all the essential background in mathematics, and contains many algorithms, some of which appear here for the first time in print. Accommodation is made for readers interested primarily in the mathematical parts, and for those who just want to implement the algorithms as quickly as possible.