Paul Halmos will celebrate his 75th birthday on the 3rd of March 1991. This volume, from colleagues, is an expression of affection for the man and respect for his contributions as scholar, writer, and teacher. It contains articles about Paul, about the times in which he worked and the places he has been, and about mathematics. Paul has furthered his profession in many ways and this collection reflects that diversity. Articles about Paul are not biographical, but rather tell about his ideas, his philosophy, and his style. Articles about the times and places in which Paul has worked describe people, events, and ways in which Paul has influenced students and colleagues over the past 50 years. Articles about mathematics are about all kinds of mathematics, including operator theory and Paul's research in the subject. This volume represents a slice of mathematical life and it shows how many parts of mathematics Paul has touched. It is fitting that this volume has been produced with the support and cooperation of Springer-Verlag. For over 35 years, Paul has contributed to mathematics publishing as founder and editor of many outstanding series.

During his short life Oswald Teichmuller wrote 34 papers, all reproduced in this volume. From the Preface: "Teichmuller's most influential paper was called "Extremale quasikonforme Abbildungen und quadratische Differentiale" (No. 20 in this collection). At the time of its appearance several special cases of extremal problems for quasiconformal mappings had already been solved, and Teichmuller was able to draw on a substantial fund of experience. Nevertheless, it was a remarkable feat to extract the common features of all the known examples and formulate a conjecture, now known as Teichmuller's theorem, which in an unexpected way connects the holomorphic second order differentials on a Riemann surface with the extremal quasiconformal mappings of that surface. The paper of 1939 contains a uniqueness proof, which is essentially still the only known proof, but not yet a rigorous existence proof. This did not prevent Teichmuller from laying the foundation of what has become known as the theory of Teichmuller spaces, a theory that has mushroomed to an extent that could not then have been foreseen. At the same time Teichmuller's work led to a deeper understanding of the fundamental role played by quasiconformal mappings in all of geometric function theory, and it foreshadowed the subsequent development of the theory of quasiconformal mappings in several dimensions...the whole theory of analytic functions of one complex variable has been greatly enriched by the inclusion of quasiconformal mappings, much of it based on Teichmuller's seminal ideas."

The Spring 1986 Program in Geometric Function Theory (GFT) at the Mathematical Sciences Research Institute (MSRI) brought together mathe maticians interested in Teichmiiller theory, quasiconformal mappings, Kleinian groups, univalent functions and value distribution. It included a large and stimulating Workshop, preceded by a mini-conference on String Theory attended by both mathematicians and physicists. These activities produced interesting results and fruitful interactions among the partici pants. These volumes represent only a portion of the papers that will even tually result from ideas developed in the offices and corridors of MSRI's elegant home. The Editors solicited contributions from all participants in the Program whether or not they gave a talk at the Workshop. Papers were also submit ted by mathematicians invited but unable to attend. All manuscripts were refereed. The articles included here cover a broad spectrum, representative of the activities during the semester. We have made an attempt to group them by subject, for the reader's convenience. The Editors take pleasure in thanking all participants, authors and ref erees for their work in producing these volumes. We are also grateful to the Scientific Advisory Council of MSRI for sup porting the Program in GFT. Finally thanks are due to the National Sci ence Foundation and those Universities (including Cornell, Michigan, Min nesota, Rutgers Newark, SUNY Stony Brook) who gave released time to faculty members to participate for extended periods in this program."

The Spring 1986 Program in Geometric Function Theory (GFT) at the Mathematical Sciences Research Institute (MSRI) brought together mathe maticians interested in Teichmiiller theory, quasiconformal mappings, Kleinian groups, univalent functions and value distribution. It included a large and stimulating Workshop, preceded by a mini-conference on String Theory attended by both mathematicians and physicists. These activities produced interesting results and fruitful interactions among the partici pants. These volumes represent only a portion of the papers that will even tually result from ideas developed in the offices and corridors of MSRI's elegant home. The Editors solicited contributions from all participants in the Program whether or not they gave a talk at the Workshop. Papers were also submit ted by mathematicians invited but unable to attend. All manuscripts were refereed. The articles included here cover a broad spectrum, representative of the activities during the semester. We have made an attempt to group them by subject, for the reader's convenience. The Editors take pleasure in thanking all participants, authors and ref erees for their work in producing these volumes. We are also grateful to the Scientific Advisory Council of MSRI for sup porting the Program in GFT. Finally thanks are due to the National Sci ence Foundation and those Universities (including Cornell, Michigan, Min nesota, Rutgers Newark, SUNY Stony Brook) who gave released time to faculty members to participate for extended periods in this program."

Paul Halmos will celebrate his 75th birthday on the 3rd of March 1991. This volume, from colleagues, is an expression of affection for the man and respect for his contributions as scholar, writer, and teacher. It contains articles about Paul, about the times in which he worked and the places he has been, and about mathematics. Paul has furthered his profession in many ways and this collection reflects that diversity. Articles about Paul are not biographical, but rather tell about his ideas, his philosophy, and his style. Articles about the times and places in which Paul has worked describe people, events, and ways in which Paul has influenced students and colleagues over the past 50 years. Articles about mathematics are about all kinds of mathematics, including operator theory and Paul's research in the subject. This volume represents a slice of mathematical life and it shows how many parts of mathematics Paul has touched. It is fitting that this volume has been produced with the support and cooperation of Springer-Verlag. For over 35 years, Paul has contributed to mathematics publishing as founder and editor of many outstanding series.