This textbook has been designed to cover the core mathematics requirements for undergraduate computer science students. The text follows a straightforward progression from the basic mathematical concepts covered by the GCSE to more sophisticated concepts which are illustrated with examples and exercises. Hints and solutions are provided for all brain-teasers listed in the book. Topics include logic and the nature of mathematical proof, set theory, relations and functions, matrices and systems of linear equations, algebraic structures, Boolean algebras and graph theory.