Fluid type lattice gas automata are discrete dynamical systems developed originally to simulate macroscopic processes occurring in real fluids. Subsequently, lattice gas automata have proven valuable as idealized models for the investigation of many-body dynamics over a wider range of space and time scales. The objective here is to formulate the statistical mechanics if lattice gas automata and illustrate it with some applications. To facilitate a close correspondence to the highly developed methods of non-equilibrium statistical mechanics for real fluids, a corresponding linear Liouville formulation of the lattice gas automata dynamics is given. The applications of this formulation described here are: a formal derivation of linear hydrodynamics and identification of Green-Kubo expressions for transport coefficients, and a description of linear kinetic theory for equilibrium fluctuations beyond the Boltzmann approximation.