In inhomogeneous systems, such as due to some internal or externally imposed gradient of some intensive parameter, a flux of the corresponding associated extensive variable is created and governed, to leading order, by Fick’s law. Associated with conservation laws, this leads to diffusion equations. Several cases are considered such as those associated with particle or mass or heat flows. In this chapter the elementary kinetic theory is presented. Also, some examples of heat flow in different geometries and boundary conditions are detailed. The motion of a Brownian particle is considered and the Einstein relation for the diffusion constant at thermal equilibrium is presented. Since processes are generally irreversible, the production of entropy is discussed, entropy current is introduced, and a short discussion of the Onsager coefficients is presented. Taking in account external fields and interactions (collisions) between particles in a macroscopic system, the Boltzmann equation for the distribution function in phase space and time is derived. The Boltzmann entropy is briefly discussed in the context of the H-theorem and its relation to time evolution and the second law of thermodynamics.