A transcendental number is a complex number which is not a root of a polynomial f E Z[X] \ {O}. Liouville constructed the first examples of transcendental numbers in 1844, Hermite proved the transcendence of e in 1873, Lindemann that of 1'( in 1882. Siegel, and then Schneider, worked with elliptic curves and abelian varieties. After a suggestion of Cartier, Lang worked with commutative algebraic groups; this led to a strong development of the subject in connection with diophantine geometry, including Wiistholz's Analytic Subgroup Theorem and the proof by Masser and Wiistholz of Faltings' Isogeny Theorem. In the meantime, Gel'fond developed his method: after his solution of Hilbert's seventh problem on the transcendence of afJ, he established a number of estimates from below for laf - a21 and lfillogal - loga21, where aI, a2 and fi are algebraic numbers. He deduced many consequences of such estimates for diophantine equations. This was the starting point of Baker's work on measures of linear independence oflogarithms of algebraic numbers. One of the most important features of transcendental methods is that they yield quantitative estimates related to algebraic numbers. This is one of the main reasons for which ''there are more mathematicians who deal with the transcendency of the special values of analytic functions than those who prove the algebraicity" I. A first example is Baker's method which provides lower bounds for nonvanishing numbers of the form lat!·· .