This account of elliptic differential equations and obstacle problems is dedicated to the memory of \n Guido Stampacchia\en. It provides a good survey for prospective researchers in the area, although the author makes no claim of completeness.

Chapter 1 sets out the relevant function space background, including a treatment of Morrey, John-Nirenberg and Campanato spaces. In Chapter 2 the variational theory of elliptic boundary value problems is presented. Regularity, estimates of solutions and their derivatives, and questions of uniqueness are discussed in Chapter 3, with particular emphasis given to the simplifying approach of Campanato. Chapter 4 is devoted to variational inequalities for both linear and nonlinear operators, with appropriate treatment of existence, uniqueness and regularity. Finally, nonvariational obstacle problems are analysed in Chapter 5.

Instructive sets of problems follow each chapter, and there are extensive bibliographical notes and references.
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