This book provides essential foundations of mathematics, covering set theory, algebra, the theory of real and complex numbers, as well as topology. It serves as a basis for further engagement with mathematics. Not only are the necessary terms introduced, but also significant - and even deeper - statements about them are proven. The material is illustrated and complemented by unusual examples and a variety of exercises. The book is suitable for self-study, but is primarily designed as a companion reading from the very beginning for studies in mathematics, physics, and computer science. Its rigorous approach makes it easy to read and comparatively easy to understand.