Mr. Tumnus is a Faun—a creature that is human from the waist up and a goat from the waist down. We want to make one thing perfectly clear: as a faun, Mr. Tumnus is a peaceful woodland dweller, not a crazed sex maniac like a satyr (the other mythological human/goat cross).
Mr. Tumnus is the first person Lucy meets in Narnia and they quickly become besties. Although Mr. Tumnus had previously agreed to hand over any human being he met to the White Witch, as soon as he meets Lucy and gets to know her, he realizes that he can't do any such thing. Mr. Tumnus suffers for protecting Lucy; he is arrested by Fenris Ulf, the Chief of the White Witch's Secret Police, and the White Witch turns him into stone. He's rescued by Lucy and Aslan when they invade the Witch's home and free the prisoners, and he becomes a valued advisor to the young Kings and Queens of Narnia.
Mr. Tumnus in Narnia, like the Professor back in England, is a single, scholarly fellow who admires the virtues of the children, especially Lucy. We get a hint that Mr. Tumnus is educated; when Lucy first sees his cave, she notices a shelf of books that have:
[...] titles like The Life and Letters of Silenus or Nymphs and Their Ways or Men, Monks, and Gamekeepers; a Study in Popular Legend or Is Man a Myth? (2.23)
Of course, part of what these titles are meant to suggest is that Lucy's world seems just as strange and mythical to Mr. Tumnus as his world does to her. However, they also make Mr. Tumnus's cave seem like a scholar's study—probably quite a bit like the kind of study or office that C.S. Lewis himself would have worked in.
Mr. Tumnus's education, though, is more literary than practical. We have to remember that Mr. Tumnus is confused by Lucy's explanation of where she came from and tells her that,
"[...] if only I had worked harder at geography when I was a little Faun, I should no doubt know all about those strange countries." (2.14)
So, although Mr. Tumnus's environment and behavior remind us of C.S. Lewis's own, he is also a distinct character with a lot of his own limitations.