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. 9 Illustrations, black and white; XVI, 354 p. 9 illus.; 9 Illustrations, black and white; XVI, 354 p. 9 illus.