This book deals with the kinetic modelling of gas mixtures. It extends the existing literature in mathematics for one species of gas to the case of gas mixtures. This is more realistic in applications. The presented model for gas mixtures is proven to be consistent meaning it satisfies the conservation laws, it admits an entropy and an equilibrium state. Furthermore, we can guarantee the existence, uniqueness and positivity of solutions. Moreover, the model is used for different applications, for example in plasma physics, for fluids with a small deviation from equilibrium and in the case of polyatomic gases.