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The book "Living Mathematics" by the world-famous science populariser Y.I. Perelman is one of the last in his series of books dedicated to fascinating science. However, after that it was considered by the author as a kind of introduction to these books. Consisting of a large number of heterogeneous puzzles, interesting stories and practical advice with a mathematical basis, the book opens the curtain to some universal methods of reasoning characteristic of mathematics as a science. No special preparation is required to read the book. Many of the puzzles can be solved by clever pupils even in primary school, although some of them may be difficult for a well-known scientist to solve. The book has been translated into many languages, including Ukrainian. The new Ukrainian translation eliminates the gaps of the previous ones, in particular, it fully restores the author's content from the lifetime editions and more carefully reflects the stylistic features of the established Ukrainian-language constructions. The book is intended for anyone who enjoys intellectual entertainment in their leisure time. It will be especially useful for students who care about developing their mathematical intelligence and expanding their mathematical knowledge.