Abstract: Symmetries and conserved quantities are treated within the framework of dynamics of particles in theoretical mechanics. A brief historical retrospect clarifies that Noether's general mathematical conclusion on symmetries and conserved quantities are mainly interpreted in classical mechanics as the correspondence between the homogeneity and isotropy of space and time and the conservation of momentum, angular momentum, and mechanical energy. The theorem of momentum, the theorem of angular momentum, and the theorem of kinetic energy are respectively applied to demonstrate that for a potential system, if the potential energy remains unchanged under coordinate translation, the system's momentum is conserved; if unchanged under coordinate rotation, the system's angular momentum is conserved; and if unchanged under time translation, the system's mechanical energy is conserved. Finally, an example is presented to illustrate that momentum conservation can still occur even in the absence of spatial translation invariance.