J.R.R. Tolkien’s first published book of imaginative fiction was The Hobbit.
The Hobbit was published in 1937 and was Tolkien’s first major book for a general reading audience. Before it appeared, Tolkien had published scholarly work and articles, including studies of medieval and Old English literature, but The Hobbit brought his storytelling to a broad public.
The novel follows Bilbo Baggins as he joins Thorin Oakenshield’s company on a quest to reclaim the Lonely Mountain from Smaug. It introduced many elements later central to Tolkien’s legendarium, including Hobbits, the Shire, the wizard Gandalf, and the One Ring.
The Lord of the Rings was published later, in three volumes between 1954 and 1955. The Silmarillion appeared only after Tolkien’s death, while Farmer Giles of Ham was a later shorter work. Those books therefore cannot be the answer to Tolkien’s first published imaginative book.