Cryptography, the art of secret writing, plays a central role in cyberspace security. In fact, one of the main driving forces of the development of modern cryptography is cyberspace security. Thus the main purpose of this book is to provide the basic theory, techniques, and algorithms of modern cryptography that are applicable to cyberspace security. The book consists of nine main chapters. Chapter 1 provides some basic concepts of cyberspace, cyberspace security, and their relation to cryptography. Chapters 2 and 3 present the basic concepts and results of mathematical and computational preliminaries that are useful and fundamental to cryptography. Chapter 4 discusses the history, techniques, and algorithms for secret-key (symmetric-key) cryptography and cryptanalysis, whereas Chaps. 5, 6, and 7 discuss the three most popular types of public-key cryptography based on the integer factorization problems, the discrete logarithm problem, and the elliptic curve discrete logarithm problem, respectively. Chapter 8 gives an account of some quantum-safe cryptographic systems that remain secure even with the presence of quantum computers. The last chapter, Chap. 9, discusses the basic ideas, techniques, and systems in offensive (malicious) cryptography, including malware extortion, malware espionage, and kleptography, based on cryptovirology.