Analytical mechanics is an advanced form of Newtonian mechanics, where the fundamental equations of motion are formulated in a modern and sophisticated mathematical way. This modern approach aims for a deep understanding of the mechanics of material points or a rigid body using only the appropriate and necessary coordinates for the problem. This new method also demonstrates how to directly link the mechanics of the groups of material points with continuum mechanics. Furthermore, analytical mechanics contributes to possibility of introducing new modifications that lead to quantum mechanics and other theories.