Cryptography, secret writing, is probably as old as writing itself. But only recently has it become the object of extensive scientific studies. Vast new applications to data security are one explanation for this. Perhaps a more important reason for the huge growth of scientific research on cryptography is the seminal idea of public-key cryptography and the resulting new vistas on the possibilities of communication. This book gives a broad overview of public-key cryptography, covering its essence and advantages, various public-key cryptosystems and protocols. It also gives a comprehensive introduction to classical cryptography and cryptanalysis. The book is self-contained and suitable both as a text and as a reference. It starts from the beginning but also includes some 1989 developments. The presentation is in many ways new, with some new results. The treatment is rigorous but avoids unnecessary formalism. The plaintext examples in the book form a package of basic sauna knowledge.