This chapter introduces Newton’s laws, the Newtonian formulation of mechanics and key concepts such as configuration space and phase space for later development. In 1687, the natural philosopher Sir Isaac Newton published the Principia Mathematica and, with it, sparked the revolutionary ideas key to all branches of classical physics. In this chapter, the system is the object of interest and is considered to be either a single or a collection of generic particles that are not governed by quantum mechanics, for quantum systems do not follow these laws explicitly. Results for systems of particles and conservation laws are presented as the invariance of a given quantity under time evolution. The N-body problem, first integrals, initial value problems and Galilean transformations are all introduced and the Picard iteration and the Verlet algorithm are discussed.