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This updated and introductory text approaches integration via measure as opposed to measure via integration, an approach which makes it easier to grasp the subject. Apart from its central importance to pure mathematics, the material is also relevant to applied mathematics and probability, with proof of the mathematics set out clearly and in considerable detail. Numerous worked examples necessary for teaching and learning at undergraduate level constitute a strong feature of the book, and after studying statements of results of the theorems, students should be able to attempt the 300 problem exercises which test comprehension, for which detailed solutions are provided. The book stems from a long-running successful course and presents the knowledge and experience of Dr. de Barra who has long taught and researched measure theory in London University. This 2nd edition has been updated by the attachment of Afternotes indicating how the subject has developed from material in the text, and misprints from the original have now been corrected. The only pre-requisite is a first course in analysis, and what little topology required is developed within the text.