In lecture 1, tasks are set and a unifocal equation of curves of the 2nd order is introduced. Lecture 2 presents the eccentricity vector, Hamilton's yearograph, and explains the process of reduction-integration. Lecture 3 presents Bertrand's problem, where we try to understand, using comments by Jacobi, Paul Serre, Appel, Kozlov and Garin, why limited orbits are closed. Lecture 4 combines several observations about the geometry of this problem, linking the constructions of Gyrgy, Jobek, Laplace and Lagrange with the eccentricity vector and with the unifocal equation. In lecture 5, Lambert's theorem is established, interesting parameters of the family of Kepler orbits passing through two points of a given plane are discussed, there is also one result K. Simo .