This book contains the proceedings of the international conference held in August 2000 at Lund University and dedicated to the sixty-fifth birthday of Jaak Peetre, one of the founders of the theory of interpolation spaces and a brilliant contributor to the progress in several other areas of mathematics. The papers in this volume cover a wide range of topics both from interpolation theory and from other fields where the ideas and results of Jaak Peetre have left an indelible mark: the theory of function spaces, Hankel-type and related operators, analysis on bounded symmetric domains, partial differential equations, Green functions, and special functions. Other papers deal with various more or less related topics such as homogenization theory, Sobolev embeddings, Coxeter groups, spectral theory and wavelets. The book starts with biographical material and a list of publications of Jaak Peetre, followed by a paper of his on the history of the ``birth'' of the theory of interpolation, and by a paper of the late co-founder of this theory, Jacques-Louis Lions, on reproducing kernels of function spaces. In addition to the latter paper, the main part of the book consists of 16 other original research papers, which contain new results with full proofs and mention interesting open problems. The book will be of interest to a wide range of readers in mathematical analysis and its applications, in particular to both researchers and graduate students interested in interpolation theory, function spaces and operators on them, partial differential equations and analysis on bounded symmetric domains.