Abstract : « In a series of groundbreaking papers published about fifty years ago, Alan Baker developed the theory of linear forms in logarithms of algebraic numbers. He proved that any expression of the form
$$\beta_0 + \beta_1 \log \alpha_1 + \cdots + \beta_n \log \alpha_n, $$
where $\alpha_1, \ldots , \alpha_n, \beta_1, \ldots , \beta_n$ are non-zero algebraic numbers
and $\beta_0$ is algebraic, vanishes only in trivial cases. He was also able to bound from below its
absolute value (when non-zero). Such estimates have numerous applications in Diophantine approximation, in the theory
of Diophantine equations, and also in various other domains. We discuss some of them.