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The goal of these lecture notes is to present the modern point of view on the classification of Fano threefolds. We tried to offer a self-consistent treatment of the topics covered. \par\medskip\noindent These notes have been published in two versions: a Russian edition in . Steklov Inst. Math., Moscow (ISBN 978-5-98419-085-5), doi: \href{https://doi.org/10.4213/lkn31}{10.4213/book1907}, and an English translation in the , , Suppl. 1 (2025), doi: \href{https://doi.org/10.1134/S0081543825020014}{10.1134/S0081543825020014}

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