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This work falls within the theory of linear forms in logarithms over acommutative linear group defined over a number field. We give lower bounds forsimultaneous linear forms in logarithms of algebraic numbers, treating both thearchimedean and $p$-adic cases. The proof includes Baker's method, Hirata'sreduction, Chudnovsky's process of variable change. The novelty is that weintegrated into the proof the modern tools of adelic slope theory, using also anew small values Siegel's lemma.

Minorations simultan\'ees de formes lin\'eaires de logarithmes de nombres alg\'ebriques