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We present a new completely effective proof of the Lindemann-Weierstrasstheorem based on algebraic independence methods. Although it is slightly weakerthan the best known estimate due to A. Sert, it improves the best estimate dueto M. Ably obtained by such methods. The novelty of the proof lies in thesimplicity of the construction of auxiliary functions, a fact that we exploitto introduce the non-specialist to methods of algebraic independence.

Une version effective du th\'eor\`eme de Lindemann-Weierstrass par des m\'ethodes d'ind\'ependance alg\'ebrique