Unveiling the dynamics of the universe

We present two methods for describing, from a pedagogical point of view, the solutions of Einstein's equations applied to a homogeneous and isotropic universe. In the first method, we define an effective gravitational potential of the universe, and the second method makes use of the fact that we can define a dynamical system of equations. The methods are applied to different cosmological models whose properties are discussed in turn. The ultimate intention is to provide simple examples to be revised in a first Cosmology course for undergraduates.