In this introductory textbook the author explains the key topics in cryptography. He takes a modern approach where defining what is meant by secure is as important as creating something that achieves that goal and security definitions are central to the discussion throughout. The author balances a largely non-rigorous style -- many proofs are sketched only -- with appropriate formality and depth. For example he uses the terminology of groups and finite fields so that the reader can understand both the latest academic research and real-world documents such as application programming interface descriptions and cryptographic standards. The text employs colour to distinguish between public and private information and all chapters include summaries and suggestions for further reading. This is a suitable textbook for advanced undergraduate and graduate students in computer science mathematics and engineering and for self-study byprofessionals in information security. While the appendix summarizes most of the basic algebra and notation required it is assumed that the reader has a basic knowledge of discrete mathematics probability and elementary calculus.