This book is aimed at illustrating that the balance equations can be derived by a method that consider the fluid-dynamic system as made up of a number of molecules. The book shows that: 1) Equilibrium/non-equilibrium is associated with the absence/presence of gradients of velocity, temperature and chemical species in the flow field. 2) In equilibrium (modelled by the Maxwell equation), both the Euler and the state equations are obtained. 3) In non-equilibrium, the equations of Newton, Fourier and Fick are obtained. Validity of these equations, therefore of the Navier-Stokes equations, is linked to the condition that the shift from equilibrium (quantified by a small perturbation of the Maxwell distribution) has to be small. 4) Considering a second order perturbation term in the distribution function produces the Burnett equations. Nowadays, the solution of rarefied flow fields relies on Direct Simulation Monte Carlo method. Four uses of the DS2V and DS3V codes have been carried out.