We consider a dilute gas of particles that collide inelastically, dissipating kinetic energy at each collision, but conserving total momentum. The collision dynamics is simplified by using a constant restitution coefficient characterizing the kinetic energy remaining after each collision. A Boltzmann equation is derived, and depends on the restitution coefficient. In isolation the gas cools, and if spatially homogeneous, it evolves to a homogeneous cooling state with a cooling rate depending on the coefficient of restitution. The distribution function then satisfies a scaling law. For many interaction potentials, this state is unstable with respect to density fluctuations. Driven granular gases are also considered, for the cases that the external forces are stochastic, or in one dimension, constant. The high energy part of the population of particles is determined for isolated and for driven gases. Rings of Saturn are discussed as an example of granular systems studied using kinetic theory.