What mathematical skills do you need to understand computers and the problems they can solve? This text introduces the basic ideas of set theory, logic and combinatorics. Intended for those who work alone and whose experiences of mathematics may have previously perhaps been somewhat intimidating, the book adopts an informal tone and chats to the reader as a well-informed friend might. In addition to its treatment of mathematical topics, it draws the attention of the reader to general patterns of thought, some of which constitute useful problem-solving skills that may be used in other domains.