Manifolds, Sheaves, and Cohomology (Springer Studium Mathematik - Master)

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.