This text makes a real effort to ease the transition from computational to theoretical maths. It is written clearly and simply, as if it is the first time a student has really had to understand a proof and the examples substantiate this with their obvious clarity and sympathetic approach. Exercises reinforce the lessons; many easy exercises at the beginning develop the students' ability and provide encouragement. This book should be of interest to degree and diploma students in departments of mathematics; assumes a grounding in calculus.