This textbook covers fundamental concepts of general dynamics and vibration theory, along with methods for developing models of the main drive systems in machine tools and other dynamic machine systems. It also presents techniques for determining the dynamic characteristics of machines and offers a comprehensive analysis of these features. Designed for students across all forms of study, it serves undergraduates in programs such as 151900.62 "Design and Technological Support of Mechanical Engineering Production" and 150700.62 "Mechanical Engineering," as well as specialists in 151001.65 "Manufacturing Technology" and master's students in 151900.68 "Design and Technological Support of Mechanical Engineering Production." The book is an essential resource for studying courses like "Metal-Cutting Machine Tools," "Calculation, Modeling, and Design of Computer-Controlled Equipment," "Mathematical Modeling in Mechanical Engineering," and "Mathematical Methods in Manufacturing Technology." It also supports students during diploma projects, coursework in "Metal-Cutting Machine Tools," and master's theses.