High school students, especially those interested in mathematics, physics and engineering, often ask, 'What is "higher" mathematics?' Sometimes they discuss this and similar questions at mathematics clubs at schools.In this book I have tried to explain, in a way a high school pupil would understand, certain concepts of higher mathematics  such as the derivative, differential equation, the number e, and natural logarithm (pupils are more apt to be aware of and interested in the latter two concepts). Wherever possible, I have tried to illustrate the concepts with problems taken from physics. In addition, I have tried to show that the concepts of "higher mathematics" are mathematical reflections of actual processes, that mathematics and life are connected, not separated, and that mathematics is a growing, not an unchanging, completed science. Not all proofs and arguments are presented with complete mathematical rigour. Some arguments are presented for illustration. This method seems to me more appropriate for a general book.The book can be used by mathematics and physics clubs at school. Part of the material is taken from lectures the author gave at the request of the advisers of school mathematics clubs at the Moscow State University.