1.The Many-Doby problems for everybody. 2.Feynman diagram or how to solve the many-Body problem by means of pictures. 3.Classical quasi particles and the quantum pinball propagator. 4.Quasi particles in fermi systems. 5.Ground state energy and the vacuram amplitude. 6.Hird’s-Eye view of diagram methods in the Many-Body problem. 7.Occupation number formalism (second quantization). 8.More about quasi particles. 9.The Single-Particle propagator Re-visited. 10.Dyson’s equations, renormalization, RPA and Ladder approximations. 11.Self-consistent renormalization and the existence of the Fermi surface. 12.Ground state energy of electron gas and nuclear propagator. 13.Collective excitations and the Two-particle propagator. 14.Fermi systems at finite temperature. 15.Diagram methods in superconductivity. 16.Phonons from a Many-Body viewpoint (reprint). 17.Quantum field theory of phase transitions in Fermi systems. 18.Feynman diagrams in the Kondo problems. 19.The renormalization group.