The book "Ordinary Differential Equations with Applications to Mechanics" offers a comprehensive introduction to ordinary differential equations and their applications in mechanics. It is aimed at students and professionals who need a solid mathematical foundation to solve technical problems. The authors, Mircea Soare, Petre P. Teodorescu, and Ileana Toma, have drawn on their experiences from the University of Bucharest and the Technical University of Civil Engineering in Bucharest to bridge the gap between mathematics and technical disciplines. This new edition includes numerous improvements and updated information based on the latest research. The focus is on analytical solutions of ordinary differential equations, deliberately excluding numerical approaches. The applications are presented in a novel way to emphasize the interdisciplinary nature of the subject.