This carefully-planned and structured book approaches integration via measure, rather than measure via integration. It is the author’s experience that this approach makes the ideas easier for the reader to grasp, and is in accordance with his intention to provide an authoritative introduction to the subject. Apart from the central importance of the material in pure mathematics, it has relevance in many different branches of applied mathematics and probability. The proofs of the mathematics involved are set out clearly and in considerable detail, and should present little difficulty. Nevertheless, what the reader requires are (i) a knowledge of the basic results and (ii) an ability to apply them, then he may skip the proofs at first reading. After studying the statements of the results of the theorems and the numerous worked examples, the reader should then be able to try the exercises, over 300 of which are provided as an integral part of the book. Detailed solutions at the end of the book are included as reader’s last resort. The book serves the dual purpose of providing advanced undergraduate course, and also a reference source for those more interested in the manipulation of sums and integrals than in the proofs of the mathematics involved; it admirably achieves both objectives. The book is self-contained and the only prerequisite is a first course in analysis; what little topology is required is developed within the framework of the text.