Holomorphic foliations on complex compact surfaces

In this work we study nonsingular holomorphic foliations on compact complex surfaces and we obtain a classification of these objects. Mainly, there are two different cases : foliations on surfaces admitting a rational or elliptic fibering, and foliations on surfaces of general type. In the first case the method consists in comparing the foliation and the fibration, for exemple looking at the curve of tangencies between them. Bott's vanishing, theorem and Kodaira's work on complex surfaces will play a fundamental role. In the second case the main step is the construction of a transverse invariant metric, which, even if singular, will reduce the problem to the context of Riemannian foliations.