The book "Oscillatory matrices and nuclei and small oscillations of mechanical systems" by the authors of F. R. Gantmacher and M. G. Crane is a fascinating and in-depth study in mechanics that will be of interest to both students and professional engineers. This work is not just a textbook, but a real find for everyone who seeks to understand complex mechanical systems and their behavior under conditions of small fluctuations. The book focuses on oscillatory matrices and cores, which are key tools for analyzing the dynamics of mechanical systems. The authors examine in detail how these mathematical constructs help describe and predict the behavior of systems in a state of oscillation. The reader is immersed in a world where simple mechanical models are transformed into complex systems that require careful analysis and deep understanding. The book offers readers not only theoretical foundations, but also practical examples, which makes it especially valuable for those who want to apply the knowledge gained in practice. This work will be of interest to students of technical specialties, graduate students, as well as practicing engineers and researchers working in the field of mechanics, physics and related disciplines .. If you are interested in dynamics, vibration theory or just want to expand your knowledge of mechanical systems, then this book will become a real treasure for you. It is suitable for both beginners and more experienced readers seeking to deepen their knowledge in this field. The topics raised in the book cover a wide range of issues related to oscillatory systems. The authors discuss the principles of sustainability, methods of analysis and synthesis, as well as various approaches to solving problems related to small fluctuations. Readers will be able to learn about how to properly use oscillatory matrices to analyze complex systems, as well as how these methods are applied in various branches of science and technology. The book also touches on important aspects, such as the influence of external factors on the dynamics of systems, which makes it especially relevant in modern conditions. The style of the authors is distinguished by clarity and accessibility, which makes it easy to assimilate even the most complex concepts. F. R. Gantmacher and M. G. Crane is known for his scientific works and textbooks, which have become classics in the field of mechanics. Their previous works, such as “Linear Systems and Mechanics” and “Theory of Oscillations”, are also noteworthy and can serve as an excellent addition to the study of the topics covered in this book. “Oscillatory matrices and nuclei and small oscillations of mechanical systems” is not just a book, but a whole world in which the reader can immerse himself by exploring the laws governing the movement and interaction of objects. This work will become a reliable assistant for those who seek not only to understand, but also to apply knowledge in real tasks. If you are looking for literature that will help you understand complex mechanical systems and open new horizons in your understanding of dynamics, this book is exactly what you need. Do not miss the opportunity to expand your horizons and deepen your knowledge in the field of mechanics with the help of this remarkable work.