In this chapter, the most widespread forms of differential equations of particle motion are presented, key theorems of particle dynamics are proved, and the conservative force field is studied. Further on, the derivation of Lagrange equations of the second kind and canonical equations for a particle makes it possible to generalize them to the motion of a system of mass points with the help of the notion of representation point. The main cases of oscillatory motion of a particle, those of motion of a particle subject to central forces as well as dynamics of the particle relative motion are analyzed in detail.