From the reviews of the second edition: "The new methods of complex manifold theory are very useful tools for investigations in algebraic geometry, complex function theory, differential operators and so on. The differential geometrical methods of this theory were developed essentially under the influence of Professor S.-S. Chern's works. The present book is a second edition... It can serve as an introduction to, and a survey of, this theory and is based on the author's lectures held at the University of California and at a summer seminar of the Canadian Mathematical Congress.... The text is illustrated by many examples... The book is warmly recommended to everyone interested in complex differential geometry." #Acta Scientiarum Mathematicarum, 41, 3-4#

Easily accessible Includes recent developments Assumes very little knowledge of differentiable manifolds and functional analysis Particular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)

The theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomology, and fiber bundle theory. As such, it is a fundamental and an essential tool in the study of differentiable manifolds. In this volume, the authors provide a thorough introduction to characteristic classes, with detailed studies of Stiefel-Whitney classes, Chern classes, Pontrjagin classes, and the Euler class. Three appendices cover the basics of cohomology theory and the differential forms approach to characteristic classes, and provide an account of Bernoulli numbers. Based on lecture notes of John Milnor, which first appeared at Princeton University in 1957 and have been widely studied by graduate students of topology ever since, this published version has been completely revised and corrected.

This volume contains the articles contributed to the Minnesota Con ference on Complex Analysis (COCA). The Conference was held March 16-21, 1964, at the University of Minnesota, under the sponsorship of the U. S. Air Force Office of Scientific Research with thirty-one invited participants attending. Of these, nineteen presented their papers in person in the form of one-hour lectures. In addition, this volume con tains papers contributed by other attending participants as well as by participants who, after having planned to attend, were unable to do so. The list of particip ants, as well as the contributions to these Proceed ings, clearly do not represent a complete coverage of the activities in all fields of complex analysis. It is hoped, however, that these limitations stemming from the partly deliberate selections will allow a fairly com prehensive account of the current research in some of those areas of complex analysis that, in the editors' belief, have rapidly developed during the past decade and may remain as active in the foreseeable future as they are at the present time. In conclusion, the editors wish to thank, first of all, the participants and contributors to these Proceedings for their enthusiastic cooperation and encouragement. Our thanks are due also to the University of Min nesota, for offering the physical facilities for the Conference, and to Springer-Verlag for publishing these proceedings.