This book was born from the notes of the analytical mechanics course and is the result of our six years of continuous teaching to second-year students of the Department of Physics at the National and Kapodistrian University of Athens. The course in analytical mechanics, along with Newtonian mechanics, which is taught beforehand, represents the first encounter of Physics Department students with theoretical physics, in the sense that the physical world is treated as a unified logical structure governed by laws, which in turn stem from fundamental principles characterized by simplicity and particular aesthetic elegance. These laws and principles are articulated with absolute clarity in the language of mathematics, and one can prove propositions and conclusions concerning physical quantities with the same rigor and consistency that characterizes purely mathematical propositions.