It's a bit sad, because I don't recall Tolkien using the word 'race' very much at all. When he does, it is in a context which implies that race in Middle Earth is more about what kind of Elf, Dwarf, Hobbit or Man you are. Gimli talks about Durins' race, meaning the Longbeards. Legolas defines himself as being of the Sylvan race, as opposed to the Noldorin Elves of Hollin, and Aragorn talks about being of the Numenorean race. Elves, Dwarfs and Men are not 'races' but 'peoples' or 'folk' - possibly because Tolkien disliked the coldly scientific implications of 'species'.