The book addresses the mathematical theory as well as applications of linear eigenoscillations, forced and parametrically excited vibrations of mechanical and non-mechanical systems. The systems examined have either a finite number of degrees of freedom or take the form of continuous strings and rods, or they are couplings of these two types of systems. The book is characterized by a pedagogically skillful presentation of the material, which clearly highlights connections between the topics of different chapters and reduces complex problems to elementary issues from the first chapter.