Kaehler manifolds: Real and complex manifolds Hodge theory Kodaira's embedding theorem

The book contains a highly focused introduction into real and complex Hodge theory including famous theorems of Kodaira as his vanishing theorem and his embedding theorem. The latter characterises all compact complex manifolds which can be embedded into some projective space as algebraic sub-manifolds. Some results as the main theorem about elliptic differential operators or the Lemmas of Poincare and Dolbeault are stated without proof. From the beginning we use a sheaf theoretic language. For the convenience of the reader we give in the appendices a complete introduction into sheaf theory in a way that can be used also in other geometric theories as for example in algebraic geometry.