The present book tells the story of a celebrated theorem and an intriguing conjecture: Markov's theorem from 1879 and the uniqueness conjecture formulated by Frobenius in 1913. The author takes the opportunity to look at this theorem and this conjecture from many different viewpoints, including Farey fractions, the modular and the free groups, the hyperbolic plane and combinatorics on words. He offers a journey through the mathematical world around Markov's theorem in a leisurely and relaxed style, making his book very pleasant to read.
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