This text provides a fresh approach to the fundamental role of powerful mathematics in modern cryptography while introducing programming concepts in Java-a language designed for system security. The text targets undergraduates in introductory cryptography courses who have a working knowledge of Java. Bishop (Grinnell College) offers online Java applets to demonstrate important concepts as readers learn to program cryptography algorithms from the ground up. Topics include large integer computing, linear cyphers, matrix cyphers, primality testing, and establishing keys and message exchange.