The thesis gives a further step in the generalizations of the theorem of Lie, which have been already generalized by Saint-Donat, Griffíths, Henkin and Passare. He also gives applications of this theorem to characterization of complete intersection families, and goes further in the case of plane curves with the study of linear systems. He concludes with an application of the Abel's theorem to the construction of a domain with Levi-flat boundary on some "strongly singular" projective variety, which intersects every projective variety of complementary dimension.