This article studies structural-semantic and compositional aspects of the poetic anagram, which reflects the cognitive and linguistic picture of the world, as well as the national conceptual sphere. It is noted that the anagram genre originated in Russian poetry in the 1820s on the pages of the magazine “Blagonamerenny”. It published the first theoretical justification of such enigmatic genres as a riddle, a logogriff, a charade and a homonym. Its author was the famous statesman N. F. Ostolopov. It was he, as well as other poets, who actively collaborated with “Blagonamerenny”, who tested and introduced into the everyday life the genre varieties of the anagram: homonymanagram, charade-anagram, anagram-logogriff. They were not only a part of the poetic experiment, but also reflected the literary life of the era and had a polemical orientation. In order to decipher the coding part of these enigmatic texts, the addressee had to have a common with the addressee level of cognitive and linguistic thinking. At the same time, a distinctive feature of the anagram genre is its dialogical structure (subject-addressing system). Besides, the compelling (imperative) formulations are integral compositional elements, which serve as an appeal to the reader, where the author gives the necessary recommendations for the correct conversion of the encoded description. The author proposes first classifications of anagrams based on the ways of representing enigmatics (encrypted words) and on the methods of creating the coding part (interpretation field). There is a conclusion that the anagram is a culturally marked type of the text, characterized by stereotypical nature, associativity, precedence, semantic completeness, direct transformation of the encrypted meaning.