Multi-collision theory for educated pedestrians

The aim of the paper is to present the linear transport theory in a form which can be easily accessible also to person with a basic graduate knowledge in mathematics and physics. The time dependent linear Boltzmann equation is approached using a multi-collision methodology and the solution for each propagation direction is sought via classical methods used for linear ODE, such as Laplace transform and Green's function method. Some results that can be fully managed analytically are presented and a general strategy for the numerical implementation proposed.