. - In this paper, we give a self-contained introduction to the mould formalism of J. Écalle. We provide a dictionary between moulds and the classical Lie algebraic formalism using non-commutative formal power series. We review results by J. Écalle and B. Vallet about the Trimmed form of local analytic diffeomorphisms of $\mathbb{C}^n$, for which we provide full proofs and details. This allows us to discuss a mould approach to the classical Poincaré-Dulac normal form for diffeomorphisms.