This manual examines in detail the main natural historical stages of the formation and development of science, questions of the philosophy of science and natural science, fundamental concepts, principles and provisions of classical mechanistic and thermodynamic, non-classical field and quantum-field and post-non-classical evolutionary-synergetic and dissipative-structural natural sciences. The issues of connection between mathematics and the natural scientific reality of the world reflected by it are considered. At the end of each chapter and some of the more complex sections, summaries are given and questions for discussion are suggested. About 400 abstract topics and over 400 test questions are given to control the assimilation and certification of the theoretical material of the manual. Intended for full-time and part-time students in the humanities and socio-economic specialties of universities, as well as for students using distance learning technologies. The manual can be useful to teachers of this academic discipline and a wide range of people in other specialties and professions, including students of natural sciences and engineering specialties, anyone interested in issues of history, the formation and development of classical, non-classical and post-non-classical natural sciences, as well as problems of modern natural science time and its role in the development of science and culture.