 Smooth manifolds (definition, coordinate systems, atlases, submanifolds, examples of manifolds, mappings of manifolds)  Tangent and cotangent space to the manifold and their relationship (definitions and properties, tangent vectors of curves, tangential views, and kotečný tangent bundles)  Vector fields on manifolds and their properties (different definitions of a vector field and their relations, the Lie bracket and its properties, Frelated vector fields and their properties, oneparameter groups, flows and integral curves and their relations)  Differential forms on manifolds and their properties (definition of differential forms; pullback, the exterior product, Lie derivative, exterior derivative, contraction and their relations and properties)


C. Isham. Modern Differential Geometry for Physicists. Singapore, 1999.

D. Krupka. Matematické základy OTR.

J. Musilová, D. Krupka. Integrální počet na Euklidových prostorech a diferencovatelných varietách. SPN, Praha, 1982.

John M. Lee. Introduction to Smooth Manifolds. 2006.

M. Fecko. Diferenciálna geometria a Lieove grupy pre fyzikov. Bratislava, Iris, 2004.

M. Spivak . Calculus on Manifolds. 1965.

M. Wisser. Math 464: Notes on Differential Geometry. 2004.

O. Kowalski. Úvod do Riemannovy geometrie. Univerzita Karlova, Praha, 1995.

S. Caroll. Lecture Notes on General Relativity.
