The book "System synthesis of programs of substantiation of modern mathematics" by N. In. Mikhailova is a unique study that immerses the reader in the world of mathematical theory and its practical application. This work will be interesting for both undergraduate and graduate students studying mathematics, and for teachers who want to deepen their knowledge and methods of teaching. In his book, Mikhailov sets an ambitious task - to create a systematic approach to the justification of modern mathematical concepts. The author explores how different mathematical theories can be integrated into a single system, which allows not only to better understand the concepts themselves, but also to apply them in practice. The book covers a wide range of topics, from the basics of mathematical logic to complex theorems and their applications in real life. This makes it especially valuable for those who want not only to study mathematics, but also to understand its deep connections with other sciences. Topics raised in the book range from philosophical questions about the nature of mathematics to practical aspects of its application in various fields such as physics, economics, and computer science. Mikhailov focuses on the importance of systems thinking in mathematics, which allows the reader to see how individual elements of the theory can be related to each other and how they affect our understanding of the world around us. This is especially true in today's world, where mathematics is becoming an integral part of technology and science. The book will be of interest not only to professional mathematicians, but also to those who just want to expand their horizons. Students, graduate students, teachers, as well as lovers of science will find in it a lot of useful ideas and concepts. If you are interested in topics such as mathematical logic, set theory or applied mathematics, then this work will be a real find for you. It will help you not only to deepen your knowledge, but also to develop the critical thinking necessary to analyze complex mathematical problems. Style N. In. Mikhailov is distinguished by clarity and accessibility, which makes his book attractive to a wide audience. The author masterfully balances between theory and practice, providing the reader with not only theoretical foundations, but also examples of their application. This allows readers not only to absorb the material, but also to apply it in their research or teaching practice. The book "Systematic synthesis of programs of substantiation of modern mathematics" is not just a textbook, but a whole world in which the reader can immerse himself to discover new horizons of mathematical knowledge. It will be a great addition to the library for anyone who wants to deepen their knowledge of mathematics and its applications. If you are looking for literature that will help you better understand modern mathematics and its place in our world, then book H. In. Mikhailova is exactly what you need . Do not miss the opportunity to get acquainted with this fascinating and informative work, which will certainly leave a mark in your understanding of mathematics and its role in science and life.