This book develops elementary classical mechanics in a setting that is appropriate for beginning university mathematics students without requiring a background in physics. It is an ideal first look at the subject for those who will go on to study more advanced aspects of the subject, such as Lagrangian, Hamiltonian, and quantum mechanics. These more advanced developments of mechanics are at the forefront of research in modern mathematics. Certainly, topics such as symplectic geometry, Lagrangian intersection theory, spectral theory, pseudodifferential operators, etc. do not require a background in classical mechanics, but studies in these areas are greatly enriched by a knowledge of their roots and how some of their motivational issues arose.