This textbook covers all the main sections of ¿Analytic geometry¿. It consists of seven chapters. First chapter explains the coordinates method which is one of the basic research methods of analytic geometry and with its help the solution of basic problems of analytic geometry. Second chapter widely explains the solution of systems of linear equations in two and three variables by using second and third order determinants. Although this chapter has an assisting character for the following chapters, it is of especial importance in studying of higher order determinants and system of linear equations of general form. Third chapter is dedicated to vector algebra. Here, linear operations on vectors, linear dependency of vectors, dot, cross and mixed products of vectors are discussed extensively. Fourth chapter is dedicated to coordinate transformations on a plane and in space, as well as line and surface equations. Knowledge acquired in this chapter is widely applied in studying of second order algebraic line and surface equations. In fifth chapter the straight line and surface equations are given as first order algebraic line and surface equations.