I Smooth Lie group actions on manifolds -- 1 Generalities -- 2 Equivariant tubular neighborhoods and orbit types decomposition -- 3 Examples: 2 and 3-dimensional S1-manifolds -- II Symplectic geometry -- 1 Symplectic manifolds -- 2 Hamiltonian vector fields and Poisson manifolds -- 3 Symplectic and hamiltonian actions -- III Morse theory for hamiltonians -- 1 Critical points of almost periodic hamiltonians -- 2 Morse functions (in the sense of Bott) -- 3 Connectivity of the fibers of the moment map -- 4 Application to convexity theorems -- IV About manifolds of this dimension -- 1 Characterisation of those circle actions which are hamiltonian -- 2 Symplectic reduction of the regular levels for a periodic hamiltonian -- 3 Blowing up fixed points; creation of index 2 critical points -- 4 4-manifolds with periodic hamiltonians -- 5 Plumbing -- A Appendix: compact symplectic SU(2)-manifolds of dimension 4 -- B Appendix: 4-dimensional S1-manifolds with no invariant symplectic form (examples) -- V Equivariant cohomology and the Duistermaat-Heckman theorems -- 1 Principal and universal bundles -- 2 The Borel construction and equivariant cohomology -- 3 Equivariant cohomology and hamiltonian actions -- 4 Duistermmat-Heckman with singularities -- 5 Localisation at fixed points -- 6 The Duistermaat-Heckman formula -- A Appendix: some algebraic topology -- B Appendix: various notions of Euler classes -- VI Toric manifolds -- 1 The action of TNC and its subgroups on CN -- 2 Fans and toric varieties -- 3 Fans, symplectic reduction, convex polyhedra -- 4 Properties of the toric manifolds X? -- 5 Complex toric surfaces -- References