教學目標： It will be of fundamental importance for students intending to specialize in differential geometry, geometric analysis, global PDEs, differential topology or dynamical systems. This will be a fairly standard course in smooth manifolds and their geometry.
課程概述：The course is designed for a variety of graduate students having widely varying kinds of preparation and interests. This is the part I of a two-semester course, covering the foundations of Differential and Riemannian Geometry.