Bøger i Surveys of Modern Mathematics serien

Provides accessible and systematic introductions to moduli spaces of Riemann surfaces, algebraic curves, moduli spaces of vector bundles on Riemann surfaces, moduli spaces of singularities, and compactification of a natural class of locally symmetric spaces.

Due to a broad connection with many subjects in mathematics and physics, Riemann surfaces and their moduli spaces have been intensively studied and will continue to attract attention in years to come. Recently, there has been an explosion of interest in and work on tropical algebraic curves. This book is an accessible introduction to all these topics.

Presents two sets of never-before-published notes from lectures given by S.-S. Chern. Differential Manifolds gives a smooth and rapid introduction to differential manifolds and differential geometry; Lectures on Integral Geometry is an accessible introduction to that subject.

Presents a set of never-before-published notes from lectures given by S.-S. Chern in 1951 on the topic of ""Minimal Submanifolds in a Riemannian Manifold"". Also presented are five of Chern's expository papers which complement the lecture notes and provide an overview of the scope and power of differential geometry.

Constructs a theory of modular forms for families of Calabi-Yau threefolds with Hodge numbers of the third cohomology equal to one. It discusses many differences and similarities between the new theory and the classical theory of modular forms defined on the upper half plane.