This book serves as an introduction to post-quantum cryptography for students, engineers and researchers in the field of information security. The first part of the book motivates the topic by briefly introducing the elements of quantum computation, and presenting Shor's algorithm, which solves the factoring problem and the discrete logarithm problem in polynomial time. The second part of the book presents some candidates for post-quantum public-key encryption and digital signature schemes. The security of these schemes is based on the mathematical problems in coding theory, multivariate quadratic equations, and lattices, respectively. The distinguishable feature of this book is a description of the mathematical concepts underlying the security of post-quantum cryptographic schemes. The book will serve as a guidance for students, researchers and engineers, helping them to quickly grasp the subject of this prospective area of cryptography.