Finite dimensional normed vector spaces. Equivalent norms. Banach spaces.Infinite-dimensional normed vector spaces--Hamel and Schauder bases; separability. Compact linear operators on a Banach space. Complementary subspaces and the open-mapping theorem. Closed Graph theorem. Hilbert spaces. Special subspaces of and and the dual space. The completion of a normed vector space. Reflexive Banach spaces