Content and Aims of this Book Earlier drafts of the manuscript of this book (James A. Boa was then coau- thor) contained discussions of many methods and examples of singular perturba- tion problems. The ambitious plans of covering a large number of topics were later abandoned in favor of the present goal: a thorough discussion of selected ideas and techniques used in the method of matched asymptotic expansions. Thus many problems and methods are not covered here: the method of av- eraging and the related method of multiple scales are mentioned mainly to give reasons why they are not discussed...