We might be standing on the brink of another revolution in cryptography, namely if large quantum computers should be built. More and more researchers seem to think that this will happen in a foreseeable future. These computers will be able to break most of the public-key cryptology used in the world today. It is recommended by many to start the transition from conventional cryptology to the so-called ``post-quantum cryptology'', already today. This book is based on the author's lecture notes, written for courses taught at the Technical University of Denmark (DTU).