Initiation to mould calculus through the example of saddle-node singularities

13 pages. A paraître dans Rev. Semin. Iberoam. Mat. Singul. Tordesillas.International audienceThis article proposes an initiation to Écalle's mould calculus, a powerful combinatorial tool which yields surprisingly explicit formulas for the normalising series attached to an analytic germ of singular vector field. This is illustrated on the case of saddle-node singularities, generated by two-dimensional vector fields which are formally conjugate to Euler's vector field $x^2\frac{\pa}{\pa x}+(x+y)\frac{\pa}{\pa y}$, and for which the formal normalisation proves to be resurgent in~$1/x$