The principal aim of this book is to introduce university level mathematics - both algebra and calculus. The text is suitable for first and second year students. It treats the material in depth, and thus can also be of interest to beginning graduate students. New concepts are motivated before being introduced through rigorous definitions. All theorems are proved and great care is taken over the logical structure of the material presented. To facilitate understanding, a large number of diagrams are included. Most of the material is presented in the traditional way, but an innovative approach is taken with emphasis on the use of Maple and in presenting a modern theory of integration. To help readers with their own use of this software, a list of Maple commands employed in the book is provided. The book advocates the use of computers in mathematics in general, and in pure mathematics in particular. It makes the point that results need not be correct just because they come from the computer. A careful and critical approach to using computer algebra systems persists throughout the text.