This book offers an introduction to cryptology, the science that makes secure communications possible, and addresses its two complementary aspects: cryptography¿--the art of making secure building blocks¿--and cryptanalysis¿--the art of breaking them. The text describes some of the most important systems in detail, including AES, RSA, group-based and lattice-based cryptography, signatures, hash functions, random generation, and more, providing detailed underpinnings for most of them. With regard to cryptanalysis, it presents a number of basic tools such as the differential and linear methods and lattice attacks. This text, based on lecture notes from the author¿s many courses on the art of cryptography, consists of two interlinked parts.