This book provides an elementary introduction to the theory of quantum computing. Its goal is to explain Shor's quantum algorithm, which will break public key cryptosystems, once large-scale quantum computers are built.\nIn 1994 Peter Shor discovered a quantum algorithm which will break most of the cryptography used in Internet communications once large scale quantum computers are built. Quantum computers are devices that operate on the principles of quantum mechanics and use quantum systems as their processors. This book introduces the exciting field of quantum computing using only high school algebra and trigonometry.We present topics from quantum mechanics, algebra, computer science and cryptography, which form the foundation of the theory of quantum computing. Understanding Shor's algorithm is one of the goals of this book.