In this chapter we introduce a notion of the point that represents a motion of mechanical system. To generate Lagrange's equations of the first and second kinds we make use of the approach demonstrating their unity and generality. This approach permits us to write Lagrange's equations in the form, which can be used both in the case of one material (mass) point and of arbitrary mechanical system with finite or infinite numbers of degrees of freedom. The notion of ideal holonomic constraints is considered from the different points of view. The connection of the obtained equations of motion with the D'Alembert - Lagrange principle is analyzed. The longitudinal motion of a car with acceleration is considered as an example of motion of a holonomic system with a nonretaining constraint.