Can mathematical modeling help in understanding biological evolution and which of the problems of evolution theory are available to mathematical analysis? This is the central problem of the book. Why is all the diversity of the living world divided into separate groups - species, varieties, etc.? Can inheritance be described without "peeping back" without using the results of an explanation? What can even be considered an explanation? These and other questions are considered in detail and almost without formulas, many examples are analyzed, various types of models and modeling principles are discussed. For everyone interested in modern biology and modeling problems - from high school students and students to specialists - biologists and mathematicians.