This chapter is aimed at introducing in an elementary yet rigorous way the mathematical properties of the Newtonian gravitational field together with the Second Law of Thermodynamics, upon which stellar dynamics is founded. We begin from the gravitational field of a point mass, and then we move to consider the field of extended mass distributions by using the superposition principle. A direct proof of Newton’s First and Second theorems for homogeneous shells is worked out, followed by a different derivation based on the Gauss theorem.