This book gives an introduction to modern geometry. Starting from an elementary level the author develops deep geometrical concepts, playing an important role today in contemporary theoretical physics. He presents various techniques and viewpoints, thereby showing the relations between the alternative approaches. At the end of each chapter suggestions for further reading are given to allow the reader to study the touched topics in greater detail. This second edition of the book contains two additional more advanced geometric techniques - the modern language and modern view of Algebraic Geometry, and Mirror Symmetry. The book grew out of lecture courses. The presentation style is therefore similar to a lecture.

Introduction to modern geometry Presenting various techniques applied in the theoretical physics Additional topics of the second edition are the modern language and modern view of Algebraic Geometry and Mirror Symmetry: Starting from an elementary level the book develops deep geometrical concepts, which play a major role in theoretical physics Written with an pedagogical approach and structured in the style of a lecture Contains suggested further reading at the end of each chapter

Autorentext
Martin Schlichenmaier is full professor for mathematics at the University of Luxemburg. He has held several teaching and research positions in the mathematics department of the University of Mannheim.

Inhalt
Manifolds.- Topology of Riemann Surfaces.- Analytic Structure.- Diffierentials and Integration.- Tori and Jacobians.- Projective Varieties.- Moduli Spaces of Curves.- Vector Bundles, Sheaves and Cohomology.- The Theorem of RiemannRoch for Line Bundles.- The Mumford Isomorphism on the Moduli Space.- TopoModern Algebraic Geometry.- Schemes.- Hodge Decomposition and K¨ahler Manifold.- Calabi-Yau Manifolds and Mirror Symmetry.