This book focuses on the specific problem of mechanical vibrations, i.e. vibrations that mechanical systems can present. For that, the book covers the most important and basic aspects of mechanical vibration that can occur in 1-degree and N-degree of freedom systems. Considering the basic content of this book, it will suit undergraduate students in the Engineering area or any other students unfamiliar with the topic and willing for a didactic and clear introduction to the theme. It is assumed that the reader has some basic knowledge of the modeling of mechanical systems.