1.Introduction. 2.Classical mechanics. 3.Introduction to differential manifolds. 4.Differential equations on manifolds. 5.The tangent and cotangent bundles. 6.Covariant 2- Tensors and metric structures. 7.LaGrange and Hamiltonian mechanics for Holonomic systems. 8.Tensors. 9.Differential forms. 10.Integration of differential forms. 11.The special theory of relativity. 12.Electromagnetic theory. 13.The mechanics of rigid body motion. 14.Lie groups. 15.Geometrical models. 16.Principal bundles and connections gauge fields and classical particles. 17.Quantum effects, line bundles, and Holonomy groups. 18.Physical law fat he gauge fields.