This book is designed to be a bridge between school and university mathematics dealing mainly with the non-calculus part of first-year undergraduate mathematics. It deals with algebra, geometry and combinatorics, plus it introduces proofs. The book also provides the foundation for a number of important developments, including the basis for probability theory, vector calculus, single-subject courses on linear algebra and introductions to abstract algebra ("Groups, rings and fields") as well as the tools needed for calculus methods.