The method of moments is a common technique to reduce kinetic equations into a fluid systems. In a first step, this method is presented as a particular form of a Galerkin approximation with respect to the kinetic variables: Such a kinetic equation is rewritten in a weak form, then the test functions are restricted to a finite dimensional space and the solutions to a finite dimensional manyfold. This yields a well-posed finite dimensional problem. In a second step, the topological properties of this solution manyfold are analyzed in order to exhibit compactness properties. This property is exploited to obtain convergence results of the method towards the initial kinetic problem when the dimension of the problem, i.e. the number of moments used for the approximation, tends to infinity. Eventually, this technique is tested on a simplified homogeneous kinetic problem.