This course is intended for registered students who are training to obtain a license in mechanical engineering. The modeling of vibratory physical phenomena currently constitutes a very important tool; discrete or continuous dynamic structures governed by differential equations (D.E)on the other hand continuous dynamic structures are governed by differential partial differential equations (P.D.E), each of them requiring to know the methods used to solve them suitably. Simple examples from practical life to enrich knowledge and to bring ideas closer to long courses have been selected. This is why the course; is divided into four main chapters, of which the first chapter is devoted to free dynamic structures at 1 dof. Forced dynamic structures (harmonic excitation, periodic excitation, unspecified dynamic excitation) are treated in the second chapter. In the third chapter, the dynamic structures with several dof are well lit while the continuous dynamic structures are the subject of the fourth chapter. A good follow up!!