Dual space. Multilinear functions. Tensor product. Tenstors of first, second and third order.  Symmetric and antismmetric tensors. Tensor contraction. Wedge product. Directional derivative. Vector fields in ℝⁿ. Derivations. 1-forms, 2-forms in ℝⁿ. Exterior derivative. Closed and exact forms. Smooth manifolds. Smooth maps. Tangent vectors. Tangent space. Derivative of a smooth map. Vector fields and 1-forms on manifolds.