The book "Markov invariant geometry on state manifolds" by the authors E. A. Morozova and N. N. Chentsova is a fascinating and in-depth study that immerses the reader in the world of mathematical theory, exploring the connections between Markov processes and geometric structures. This work will be a real find for students, graduate students and researchers in the field of mathematics, statistics and theoretical physics, as well as for anyone interested in modern methods of analyzing complex systems. In their book, the authors offer the reader a unique view of Markov processes, viewing them through the prism of invariant geometry. They explore how different geometric structures can be used to describe the states of systems that are subject to random changes. In this context, state varieties become not just abstract mathematical objects, but important tools for understanding the dynamics and behavior of complex systems. The reader will be able to see how geometric approaches help in the analysis and interpretation of the results, making the book particularly relevant to researchers working in areas such as biology, economics, and physics. The book will be of interest not only to specialists, but also to those who want to expand their knowledge about Markov processes and their applications. If you are a student studying probabilistic processes, or just a math lover who wants to deepen his knowledge, this work will become a real treasure for you. The authors masterfully explain complex concepts, making them available to a wide audience, which makes reading not only informative, but also fascinating. The topics raised in the book cover a wide range of issues, ranging from the foundations of probability theory to modern approaches to data analysis. The authors emphasize the importance of invariant properties in Markov processes, which allows the reader to better understand how different systems can behave under uncertainty. This book is not just a textbook, but a real monograph that opens new horizons in understanding Markov processes and their geometric aspects. The style of the authors is distinguished by clarity and logical presentation, which allows the reader to easily follow the course of thought and absorb the material presented. E. A. Morozov and N. N. Chentsov are well-known experts in the field of probability theory and mathematical statistics, and their previous works have already established themselves as authoritative sources. Their experience and in-depth knowledge in this field make this book especially valuable for those who seek professional growth and scientific achievements. If you are looking for literature that will help you understand the complex aspects of Markov processes and their geometric interpretations, then “Markov invariant geometry on a variety of states” will become your reliable guide. This book will not only enrich your knowledge, but also inspire new research and discoveries in mathematics and its applications. Do not miss the opportunity to touch modern scientific achievements and expand your horizons with Morozov and Chentsov.