1.Introduction and basic definitions. 2.The scalar product. 3.Component representation of a vector. 4.The vector product (Axial Vector). 5.The triple scalar product. 6.Application of vector calculus. 7.Differentiation and integration of vectors. 8.The moving trihedral (accompanying Dreibein) - the Frenet formulas. 9.Surface in space. 10.Coordinate frames. 11.Vector differential operations. 12.Determination of line integrals. 13.The integral laws of Gauss and stokes. 14.Calculations of surface integrals. 15.Volume´s axioms. 16.Newton´s axioms. 17.Basic concepts of mechanics. 18.The general linear motion. 19.The free fall. 20.Friction. 21.The harmonic oscillator. 22.Mathematical interlude: differential equations. 23.The damped harmonic oscillator. 24.The pendulum. 25.Mathematical interlude: differential equations. 26.Planetary motions. 27.Special problems in central fields. 28.The earth and our solar system. 29.Relativity principle and Michelson-Morley experiment. 30.The Lorentz transformation. 31.Properties of the Lorentz transformation. 32.Addition theorem of the velocities. 33.The basic quantities of mechanics in minkowski space. 34.Applications of the special theory of relativity.