chapter 1 Basic Notions -- chapter 2 Section 2.1. Simple Morse Functions -- chapter 3 Rough Liouville Equivalence of Integrable Systems with Two Degrees of Freedom -- chapter 4 Section 4.1. Admissible Coordinate Systems on the Boundary of a 3-Atom -- chapter 5 Section 5.1. Rotation Function and Rotation Vector -- chapter 6 Section 6.1. Invariants of a Hamiltonian System on a 2-Atom -- chapter 7 Section 7.1. Constructing Smooth Invariants on 2-Atoms -- chapter 8 Orbital Classification of Integrable Hamiltonian Systems with Two Degrees of Freedom. The Second Step -- chapter 9 Section 9.1. l-Type of a Four-Dimensional Singularity -- chapter 10 Section 10.1. General Scheme for Topological Analysis of the Liouville Foliation -- chapter 11 Integrable Geodesic Flows on Two-dimensional Surfaces -- chapter 12 Section 12.1. The Torus -- chapter 13 Section 13.1. Case of the Torus -- chapter 14 Section 14.1. Integrable Cases in Rigid Body Dynamics -- chapter 15 Maupertuis Principle and Geodesic Equivalence -- chapter 16 Section 16.1. Introduction.