The Mordell-Weil theorem states that the group of rational points A(K) on an Abelian variety A/K defined over a number field is finitely generated. While there exist results on the torsion part, the free part remains less tractable. Even in the particular case of an elliptic curve, there is no way, in general, to compute the rank or a set of generators of this group. The proof of the Mordell-Weil theorem involves the Tate-Shafarevich group of A/K, which measures the obstruction to the Hasse principle. Even if it is not easy to construct a non trivial element of this group, it is still unknown, in the general case, if it is finite. For some applications, it would be sufficient to bound the « size » of the invariants related to the variety. In this article, we explore how could be bounded 1- the canonical height of a well chosen system of generators of the Mordell-weil group A(K), as well as 2- the order of the Tate-Shafarevic group of A(K). The bounds given here are not conjectured, but implied, by strong but nowadays classical conjectures. We follow the approach of Manin, who proposed a conditional algorithm for finding a basis for the non-torsion rational points of an elliptic curve over the rationals numbers. The method is based on the hypothesis that the L-series of the elliptic curve satisfies a functional equation and on the celebrated conjecture of Birch and Swinnerton-Dyer. We extend Manin's method to an Abelian variety of arbitrary dimension, defined over an arbitrary number field, extending to this general case, - with point 1, a conjecture of S. Lang , - with point 2, a result by D. Goldfeld and L. Szpiro, which we improve in the one dimensional case over the field of rational numbers.