Compact Riemann Surfaces [electronic resource] : An Introduction to Contemporary Mathematics / by Jürgen Jost.

Topological Foundations -- Differential Geometry of Riemann Surfaces -- Harmonic Maps -- Teichmüller Spaces -- Geometric Structures on Riemann Surfaces -- Erratum to: Characterizing Programming Systems Allowing Program Self-reference.

Although Riemann surfaces are a time-honoured field, this book is novel in its broad perspective that systematically explores the connection with other fields of mathematics. It can serve as an introduction to contemporary mathematics as a whole as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. It is unique among textbooks on Riemann surfaces in including an introduction to Teichmüller theory. For this new edition, the author has expanded and rewritten several sections to include additional material and to improve the presentation.