Mechanics, one of the oldest branches of science, is introduced with a brief account of contributions by Aristotle, Archimedes, Ibn Bajja, Galileo, and Isaac Newton. Galileo studied the motion of freely falling objects and measured the value of acceleration due to gravity. Newton’s laws of motion and the universal law of gravitation, which form the backbone of mechanics, are clearly presented. The chapter also covers the historical development of d’Alembert’s principle of virtual work. It describes the Lagrangian and Hamiltonian mechanics along with the variational principle. It includes a discussion on the evolution of the theory of elasticity, highlighting the contributions of Robert Hooke, Thomas Young, Woldemar Voigt, Augustin-Louis Cauchy, George Green, and others.