This is the final volume of a series covering all stages of development of the Calculus, from the last year at school to degree standard. The books are written for students of science and engineering as well as for specialist mathematicians, and are designed to bridge the gap between the works used in schools and more advanced studies, with their emphasis on rigour. Dr Maxwell guides the student through the early stages of analysis, while keeping the exposition as clear and uncomplicated as possible. The aim is to instil a knowledge of general method rather than to study the particular functions in detail; in this way the student is led on naturally to apply what they have learnt to move advanced mathematical contexts. Dr Maxwell is, as usual, lucid in his presentation, explaining difficulties in greater detail than is customary in an advanced textbook, and guarding against the pitfalls that await the beginner.