This course is intended as an introduction to the modern differential geometry. It can be taken with a view on further experience in Geometry and Topology and should also be suitable as a supplementary course if your main interests are e.g. in Analysis or Mathematical Physics.
Tentative syllabus is as follows.
Local Analysis and Differential Manifolds. Exterior algebra of differential forms. Bundle morphisms and automorphisms. Existence of connections. Parallel transport and holonomy transformation.