These lecture notes are intended as an introduction to the methods of
classification of holomorphic vector bundles over projective algebraic
manifolds X. To be as concrete as possible we have mostly restricted
ourselves to the case X = Fn. According to Serre (GAGA) the
classification of holomorphic vector bundles is equivalent to the
classification of algebraic vector bundles. Here we have used almost
exclusively the language of analytic geometry. The book is intended for
students who have a basic knowledge of analytic and (or) algebraic
geometry. Some funda- mental results from these fields are summarized at
the beginning. One of the authors gave a survey in the Seminaire
Bourbaki 1978 on the current state of the classification of holomorphic
vector bundles overFn. This lecture then served as the basis for a
course of lectures in Gottingen in the Winter Semester 78/79. The
present work is an extended and up-dated exposition of that course.
Because of the introductory nature of this book we have had to leave out
some difficult topics such as the restriction theorem of Barth. As
compensation we have appended to each sec- tion a paragraph in which
historical remarks are made, further results indicated and unsolved
problems presented. The book is divided into two chapters. Each chapter
is subdivided into several sections which in turn are made up of a
number of paragraphs. Each section is preceeded by a short description
of iv its contents.
