*FrontMatter, pg. i*Preface, pg. vii*Contents, pg. ix*Chapter I. Connections in Vector Bundles, pg. 1*Chapter II. Chern Classes, pg. 30*Chapter III. Vanishing Theorems, pg. 49*Chapter IV Einstein-Hermitian vector bundles, pg. 98*Chapter V. Stable vector bundles, pg. 133*Chapter VI. Existence of approximate Einstein-Hermitian structures, pg. 193*Chapter VII. Moduli spaces of vector bundles, pg. 237*Bibliography, pg. 291*Index, pg. 299*Notations, pg. 303