An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces: Theoretical and Mathematical Physics

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 Riemann–Roch 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.

From the reviews of the second edition:
"As the title suggests, this book is an introduction to Riemann surfaces, with the target audience being students of string theory. … an excellent book to use to become familiar with these concepts, and as a result the book is able to touch on a wide variety of concepts which are not broached by more traditional treatments of the subject. … I would certainly recommend the book for anyone who wants an enjoyable conceptual introduction to what can be a highly technical subject." (Mark Gross, Mathematical Reviews, Issue 2008 k)
"This book is an introduction to the language of modern algebraic geometry, designed mainly for Physics students who are interested in string theory. … Overall the book is very readable and it fulfills its goal remarkably well … that are useful to physicists interested in string theory, with all the necessary references for further reading. This book will be an excellent addition to the bookshelf of any physics student or researcher who wants to learn about the mathematical aspects of string theory." (Valentino Tosatti, Zentrablatt MATH, Vol. 1153, 2009)

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.

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