About 37 BCE Gaius Asinius Pollio, general, lawyer, orator, poet, friend of Virgil and Horace, and Consul in 40 BCE, having amassed a fortune in his conquest of Dalmatia and/or campaigns in Parthia, consolidated several book collections already in Rome, possibly including those of Varro and Sulla, to form a library in the Temple of Liberty (Atrium Libertatis) on the Aventine Hill.
As was standard, the Bibliotheca Asini Pollionis had Greek and Latin wings. "Public archives had already been housed there, but Pollio reorganized the collection, added the libraries he had acquired, and opened the whole to the public about 37 B.C., making it the first-known public library in Rome” (Harris, History of Libraries in the Western World 4th ed.  57.)
Clark, The Care of Books (1902) p. 12 quotes Pliny's remark about Asinius Pollio: "he was the first to make men's talents public property (ingenia hominium rem publicam fecit)."