The book "Markovian invariant geometry on state manifolds", written by well-known scientists Morozov E. A. and Chentsov N. N. It is a unique study that immerses the reader in the world of mathematical theory, exploring complex structures and processes. This publication will be of particular interest to those involved in mathematics, physics, statistics, and probability theory, as well as anyone who seeks to understand more deeply the principles underlying stochastic processes. In the book, the authors offer readers a fascinating journey through a variety of states, where each page opens up new horizons for understanding Markov processes. The main focus is on invariant properties that allow us to investigate the dynamics of systems in equilibrium. This work is not only theoretical, but also practical, as the authors illustrate their ideas with examples from various fields of science, including physics, biology and economics. The reader will find many interesting topics in the book, such as the properties of Markov processes, their application in various scientific disciplines and methods of data analysis. The author's style of Morozov and Chentsov is distinguished by clarity and accessibility, which makes complex concepts more understandable even for those who are not specialists in this field. The book is written in such a way that every reader can find something useful in it, regardless of the level of preparation. This work will be especially useful to graduate students, researchers and teachers, as well as anyone interested in modern mathematical methods and their application. It can be a great addition to the library of students and professionals working in the field of probability theory and statistics. The book will also be of interest to those who are looking for new approaches to data analysis and modeling of complex systems. The topics raised in Markov's Invariant Geometry on State Varieties are widely used in modern research. For example, the authors consider how invariant properties can help in understanding the stability of systems and their behavior under uncertainty. This makes the book relevant for researchers working in the field of machine learning and artificial intelligence, where Markov models play a key role. Morozov E . A. Chentsov N . N. are recognized experts in their field, and their previous work has already established itself as an important contribution to the scientific community Their research covers a wide range of topics, including probability theory, statistics, and mathematical physics. Readers familiar with the authors' other works will appreciate their capacity for in-depth analysis and original approach to complex issues. In conclusion, “Markov’s Invariant Geometry on State Varieties” is not just a book, but a whole world of ideas and discoveries waiting for its reader. It will become a reliable companion for all who seek to expand their knowledge in mathematics and its application in real-world problems. If you are looking for a deep and engaging reading that will not only enrich your mind, but also inspire new research, this book is your perfect choice. Do not miss the opportunity to touch on advanced ideas and concepts that can change your understanding of mathematics and its role in the modern world.