This chapter separates the treatment of non-interacting systems from that of interacting systems. The first example is a Bose liquid where the notion of a Bose condensate is replaced by that of superfluidity, due to the change of the dispersion relation in the presence of interactions. In the case of a Fermi system, the free fermion case is first replaced by the Fermi liquid concept, of essentially a renormalized Fermi gas due to the interactions and the existence of quasi-particles (weakly interacting and will-defined in the vicinity of the Fermi surface). The statistical properties of fermions lead to various effects that influence both the space part and the spin part of the wave functions. The origin of magnetic moments and the presence of direct and exchange terms are consequences. Approximate methods are introduced to solve the problem, such as the Hartree-Fock approximation. Different solutions are considered including charge and spin density waves. The effect of the Coulomb interaction is dealt with deriving the dynamical Lindhard function and screening effects and dynamical properties are presented in some detail.