Lewis Carroll loved puns, like those about the tortoise who taught us, or the lessons that lessen the need for any more of them. He especially loved puns that could be found hiding in one word, like wonderland: a place full of wonders and a place where you wonder what is happening to you. These meanings are not only different, they can be read as opposites, as Robert ­Douglas-Fairhurst reminds us, quoting a Victorian evocation of a person “who, being in a chronic state of wonder, is surprised at nothing.” Sentimental memories of the Alice books often stress the first, dazzled meaning, but a fresh reading of Carroll is likely to leave us much closer to the second, which Douglas-Fairhurst neatly formulates as “being puzzled at what we do not know.” This is how the flowers talk in “Through the Looking-Glass”: “I wonder how you do it,” a rose says to ­Alice, referring to her odd human ability to move about. “You’re always wondering,” an irritated tiger-lily says.

We are still wondering about Alice, where she came from and where she went, and Douglas-Fairhurst, the author of a well-regarded biography of Dickens, wants to inform our wonder rather than put it entirely to rest. His book doesn’t explore a great deal of new material, but it does offer a thoughtful, far-­reaching narrative, the story of three very different lives: those of Lewis Carroll, Alice Hargreaves, née Liddell, and the literary creation they both had a part in.

Late in life, Carroll referred to Alice Liddell as one “without whose infant patronage I might possibly never have written at all.” He is thinking of a trip he and a clerical friend took with the three Liddell girls — Alice was 10 at the time — up the river outside Oxford, and of Alice’s begging him to write down the story he told them then. He wrote “Alice’s Adventures Under Ground” for her, and gave her a handwritten, illustrated copy. Meanwhile he was expanding this text into what became “Alice’s Adventures in Wonderland” (1865). Alice’s role in the book’s begetting was known to her and to family members, of course, but not to anyone else much, and in 1899 Isa Bowman was able to publish a book about Carroll “told for young people by the real Alice in Wonderland” — “real” here meaning the actual actress who had appeared in a stage version of the adventures. In 1932, when Alice Hargreaves received an honorary degree from Columbia University, it had been known for some time “that there had been a real Alice, and that she was still alive,” but the news had not really sunk in, and the apparent revelation was so exciting that no one seemed to hesitate over — or wonder about — the notion of a person’s getting a degree for being a fictional character, or for nagging a writer into fame.

The Alice books are about many things, and identity is important among them. Alice worries a lot about who she is or has become, and there is much talk about growing in several senses: getting bigger, getting older, becoming an adult. “There ought to be a book written about me,” Alice says to herself. “And when I grow up, I’ll write one — but I’m grown up now.” She is crushed inside a tiny house at this point. Did Charles Lutwidge Dodgson grow into Lewis Carroll, or was there some other sort of mutation? His gravestone calls him Dodgson and puts Lewis Carroll in parenthesis. The first biography, by his nephew, does the reverse. When Alice Hargreaves died, headlines in The Times of London called her both Mrs. Hargreaves and ­Alice in Wonderland. The Evening Standard settled for Alice. ­Douglas-Fairhurst says, “What nobody outside her immediate family seemed entirely sure about was whose life had just ended,” and one might think the same of the other case. ­Douglas-Fairhurst’s ability to make room for such doubts without giving in to them is one of his book’s great attractions.