MADELEINE’S WORLD: A Child’s Journey From Birth to Age Three.<i> By Brian Hall</i> .<i> Houghton Mifflin: 262 pp., $20</i>

Brian Hall no doubt received the advice all new parents get when they start crowing about Samantha’s first steps or Zachary’s particularly telling insight at the dinner table: “You ought to write these things down.” He has done just that, with a vengeance.

In “Madeleine’s World,” however, Hall’s aim is more ambitious than simply to record milestones, poignant moments and adorable stories from his daughter’s first three years of life. He means to write an interior biography from her perspective, to wrap in a grown-up’s context the voyage from the free-fall of birth to the first sparks of preschooler reason--that is, Madeleine’s innate belief “that her brain could confront the entire cosmos; that it could contain it.”

Because Hall is an accomplished novelist (“The Dreamers,” “The Saskiad”) and travel writer (“The Impossible Country: A Journey Through the Last Days of Yugoslavia”), this enterprise can be seen on one level as a serious attempt to explore and explain a child’s world from the inside. On another, it’s a glorious excuse for a dad to talk about his kid. Viewed from that perspective, reading “Madeleine’s World” is a lot like listening to any parent--albeit one who is remarkably sympathetic and articulate--expound on the spellbinding topic of his offspring. Hall stuns with his observational powers and emotional truth, and sometimes he’s simply way more interested in the subject than we are.

Predictably, the most troublesome part of the book is in the early chapters: Infants don’t have much going in the way of consciousness, so Hall is forced to interpret her cryptic signals in ways that unintentionally tell us more about his all-consuming need to process Madeleine’s experiences than it does about the child herself. When he notes that “by four months [she] was never putting anything in her mouth except the breast, the pacifier, and her own fist, which presumably did not highlight so painfully the subject-object division,” I was seized by the desire to pass some smelling salts under the writer’s nose to snap him out of it.

But just when his bent for erecting theoretical castles around basic infant instincts seems in danger of spinning out of control, along comes a startlingly lucid (and often quite funny) perception. No parent, for instance, will ever have the same perspective on retrieving those objects constantly jettisoned from the high chair to the floor at mealtime after reading Hall’s take on the subject: “Would we return them? We would. Would we come across the room to do it? We would. Would we do it again and again? This was good science, a graduated series of tests, a determination of the parameters of natural laws.”

Once Madeleine embarks upon the twin endeavors of mobility and language, you’d expect the book to perk up. Not quite yet. Hall, who has clearly had a chummy relationship with his old linguistics textbooks, lingers at worrying length over the glacial process that leads from gibberish to articulate speech. Granted, his skill at pinpointing the connections between his daughter’s emerging consciousness and her various object identifications, coinages and mispronunciations are unquestionably impressive and occasionally illuminating. However, I could easily do without knowing the full catalog of Madeleine’s terminology for all the chairs in the house or the order in which she learned the names for colors, or that her “no” came out sounding like the Norwegian “nej” because “for some reason she had trouble reproducing the long O.” This is the sort of material that loses most of its impact when the child in question isn’t yours.

But in its second half, the book really blossoms--much as toddlers do, in fact, as their increasing mastery of the world makes it clear they’re fully vested citizens. As his relationship with his daughter passes through specimen-observer and teacher-pupil stages and becomes one between parent and child (a relationship that includes the previous elements of observation and teaching, granted, but is something altogether more convoluted and interesting), Hall’s prose becomes less clinical, more relaxed and affectionate. Madeleine makes a welcome transition from test case to child. He makes remarkably fresh, pithy and irrefutable asides, as when he notes the way toddlers incorporate their fear of abandonment into their play with adults: “The chasing game kids love is a pure draft of reassurance that they can’t get away from us even if they try.”

Of course, now that Madeleine can explain herself--well, to an extent--her father is spared the need to take on that job for her and the reader. By balancing events and conversations with his commentary, Hall succeeds dazzlingly at making his daughter and the toddler sensibility come alive on the page. Hearing her tell her mother, “I know I’m Madeleine, because I have music inside me that makes me go around, and I always come back to you” just flattens me; this is the very particular poetry of a 2-year-old preserved in amber (and all of us have known these moments with our small children, if only we could remember them). That moment alone would justify the entire book.

Not that Hall goes all mawkish. In fact, while his loving detachment (no, it’s not an oxymoron) makes Madeleine’s early months occasionally trying to the reader, this quality is exactly what enables him to prevail in the end. He tracks with elegant precision the seeds of his daughter’s awareness of death, her canny manipulation of her parents’ desire for toilet teaching, her tantrums, her profound ambivalence toward siblinghood when she gains a sister (which he incisively defines as “instinctive obedience struggling with rational rebelliousness”), all with remarkable specificity but without patly comforting conclusions. Hall recognizes that, as a friend of mine once put it: “As your child becomes complicated, so does your job.”

Like parenthood itself, “Madeleine’s World” requires a lot of patience before you can claim its immense rewards. But it is a most welcome book in a society that loudly celebrates the sentimental notion of family while paying scant attention to the hearts and minds of the messy, ecstatic, sometimes ugly and endlessly eventful lives of the children who actually make family possible.

As my own journey through Madeleine’s world progressed, I found myself seeing not only refractions of her development in my own children (our daughter is 4, our son 14 months old) but also those components that make either of them absolutely sui generis. In fact, I am now pretty certain what my son Gavin means when he says “giu,” and it’s something quite different from “gahh.” Any parent who cares about the difference between the two--and more parents ought to--will find a companionable kindred spirit in Brian Hall.