"Symplectic geometry" is an outstanding work written by two masters of mathematics, Vladimir Igorevich Arnold and Valentin Alekseevich Givental .. This book will be a real discovery for everyone who is interested not only in mathematics, but also in the philosophy of science, as well as in those areas where mathematics intersects with physics, mechanics and even art. Symplectic geometry is a branch of mathematics that studies the symplectic manifolds that play a key role in classical mechanics and dynamical systems theory. In the book, the authors present readers with complex concepts with clarity and accessibility, which makes it suitable for both students and experienced professionals seeking to deepen their knowledge in this area. The book covers a wide range of topics, ranging from the basics of symplectic geometry to its modern applications. Arnold and Givental not only expound the theory, but also illustrate it with practical examples, which allows the reader to better understand how these abstract concepts work in the real world. Readers will be able to learn about such key concepts as symplectic forms, Lagrange and Hamiltonian systems, as well as how simplectic geometry helps in solving problems related to dynamics and mechanics. This book will be especially interesting for those who are fond of mathematics, physics and engineering. Students and graduate students of mathematical and physical faculties will find it useful materials for their research, and teachers will be able to use it as a teaching aid. In addition, the book will attract the attention of those interested in interdisciplinary approaches, since symplectic geometry is used not only in mathematics, but also in such areas as quantum mechanics and theoretical physics. The style of the authors is distinguished by clarity and logical presentation, which makes complex concepts more accessible for understanding. Arnold, known for his work in differential geometry and mechanics, and Givental, who made a significant contribution to the theory of symplectic geometry, create a unique synergy that makes this book not only a textbook, but also a real work of art. The book "Symplectic Geometry" stands out among other mathematical works for its ability to combine theory and practice, making it an indispensable resource for anyone who wants to understand this fascinating section of mathematics more deeply. Readers who are looking for similar works can pay attention to books on differential geometry, dynamical systems theory, or mechanics, such as Geometry and Physics or Dynamics and Simplectic Systems. Thus, “Symplectic Geometry” is not just a book, but a whole world in which readers immerse themselves, seeking to comprehend the depths of mathematical thought and its application in the real world. This work will be an excellent addition to the library of anyone who appreciates the beauty of mathematics and its ability to explain the complex phenomena of the surrounding world.