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1 2.3.3.The case b+ = 1 2.3.4.Some examples 2.4.Applications 2.4.1.The Seiberg-Witten equations on cylinders 2.4.2.The Thom conjecture 2,4.3.Negative definite smooth 4-manifolds Chapter 3.Seiberg-Witten Equations on Complex Surfaces 3.1.A short trip in complex geometry 3.1.1.Basic notions 3.1.2.Examples of complex surfaces 3.1.3.Kodaira classification of complex surfaces 3.2.Seiberg-Witten invariants of Khler surfaces 3.2.1.Seiberg-Witten equations on Kahler surfaces 3.2.2.Monopoles, vortices and divisors 3.2.3.Deformation theory 3.3.Applications 3.3.1.A nonvanishing result 3.3.2.Seiberg-Witten invariants of simply connected elliptic surfaces 3.3.3.The failure of the h-cobordism theorem in four dimensions 3.3.4.Seiberg-Witten equations on symplectic 4-manifolds