In this course, we introduce the concept of (smooth) manifold and various useful theorems.
(1) The notion of smooth manifolds (regular values, Sard theorem, Morse function, and classification of surfaces)
(2) Degree of smooth maps.
(3) Differential forms, Calculus on manifolds, Stokes' theorem.
If there were enough time, we might discuss some applications of the above tools to some topics (Frobenius theorem, de Rham cohomology, Riemann surface, moving frame method…). 以上的中文翻譯