A modern educated person does not need to prove how important mathematics is. After all, it is not only interesting in theory, but also obviously useful in everyday life. Researchers' fascination with this science has led to countless brilliant ideas. Flipping through the pages of this book, you will remember that the numbers we are used to can be wonderful and irrational, get to know Hamilton's quaternions better and appreciate the grace of Apollonius' conical sections... And mathematical paradoxes, such as the famous walk along the seven Königsberg bridges or the search for the second side of the Möbius tape, will cheer you up. The mathematical ideas presented in this edition are retold in a simple language accessible to the widest circle of readers, which means that they will not leave indifferent all connoisseurs of this excellent science.