The subject of the book is the development of physics in the 18th century centred upon the fundamental contributions of Leonhard Euler to physics and mathematics.Classical mechanics will be reconstructed in terms of the program initiated by Euler in 1736 and its completion over the following decades until 1760. It is of particular interest to study how Euler made immediate use of his mathematics for mechanics and coordinated his progress in mathematics with his progress in physics. The interplay between physics and mathematics which appeared in the 18th century will be compared to the development of physics in the 20th century, especially to the development of quantum mechanics between 1900 and 1930. The method of investigation can be used for didactic purposes to demonstrate the relations between classical and quantum mechanics as well as the application of the calculus in physical theories.