Manifolds Sheaves and Cohomology Topological Preliminaries Algebraic Topological Preliminaries Sheaves Manifolds Local Theory of Manifolds Lie Groups Torsors and Non abelian Cech Cohomology Bundles Soft Sheaves Cohomology of Complexes of Sheaves Cohomology of Sheaves of Locally Constant Functions Appendix: Basic Topology The Language of Categories Basic Algebra Homological Algebra Local Analysis. This book explains techniques that are essential in almost all branches of modern geometry such as algebraic geometry complex geometry or non archimedian geometry. It uses the most accessible case real and complex manifolds as a model. The author especially emphasizes the difference between local and global questions. Cohomology theory of sheaves is introduced and its usage is illustrated by many examples. Content Topological Preliminaries Algebraic Topological Preliminaries Sheaves Manifolds Local Theory of Manifolds Lie Groups Torsors and Non abelian Cech Cohomology Bundles Soft Sheaves Cohomology of Complexes of Sheaves Cohomology of Sheaves of Locally Constant Functions Appendix: Basic Topology The Language of Categories Basic Algebra Homological Algebra Local Analysis Readership Graduate Students in Mathematics Master of Science in Mathematics About the Author Prof. Dr. Torsten Wedhorn Department of Mathematics Technische Universität Darmstadt Germany.