This thorough and detailed exposition is the result of an intensive month-long course on mirror symmetry sponsored by the Clay Mathematics Institute. It develop

Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential

In recent years the methods of modern differential geometry have become of considerable importance in theoretical physics and have found application in relativi

This textbook, first published in 2004, provides an introduction to the major mathematical structures used in physics today.