This book is devoted to recent advances in the modeling of collisions. It contains a series of lectures delivered by a plasma physicist Alain Decoster and two applied mathematicians Peter Markowich and Benoît Perthame. The first part, by A. Decoster, recalls how the fluid equations of a collisional plasma are deduced from the Fokker-Planck description of a kinetic plasma. The transport equations thus obtained are known for a plasma with one kind of ions (Spitzer, Braginskii). The calculation is extended here to the case of several ionic species, including the different charge states of a single atomic species. The multifluid description of plasma interpenetration is also investigated. The second part, by B. Perthame, introduces to the mathematical theory of Boltzmann's equation. It derives the Boltzmann model as the Boltzmann-Grad limit of a system of particles. The fluid limit of the Boltzmann model is also considered. The third part, by P. Markowich, studies the quantum hydrodynamic model considered recently in semiconductor simulation and presents the main mathematical features of this model.