A coming-of-age film that stands head and shoulders above most in that popular genre, “Lady Bird” represents the debut of actress Greta Gerwig as both solo writer and director (she has previously collaborated with Noah Baumbach and Joe Swanberg in those capacities), and it’s an auspicious one. Smart, incisive and emotionally satisfying, it’s both specific (being semi-autobiographical) and universal in its observations about teen angst.

Playing a character who is essentially the younger Gerwig (the film is set in 2002-2003), Saoirse Ronan is a revelation as Christine McPherson, who’s unhappy with everything—her hometown of Sacramento, which she considers stifling, her mother Marion (Laurie Metcalf), who’s bossy and (so it seems to Christine) cheap, and her school, the Catholic Eternal Flame Academy, where she and her BFF Jules (Beanie Feldstein) negotiate the campus. She even dislikes her given name, so she changes it to Lady Bird—something her loving dad Larry (Tracy Letts) accepts genially but Marion abhors. She also finds her adopted brother Miguel (Jordan Rodrigues) and his live-in girlfriend constant irritants.

Lady Bird’s major desire is to get out of town—specifically, to go to college in New York City. That seems an unlikely possibility, given that her grades are mediocre and the family finances grim (Larry has just lost his job, and Marion is working double shifts at a hospital to keep them above water). Her only bet, her mother insists during a local college tour that ends rather abruptly when Lady Bird tries to escape Marion’s nagging, is to choose a nearby school with in-state tuition. But Lady Bird, with Larry’s connivance, will nevertheless submit applications to more distant schools in hopes of getting a scholarship.

She’s also interested in romance, and finds it—she thinks—with Danny O’Neill (Lucas Hedges), a drama club star (specializing in singing roles) and all-around nice guy. For awhile that works out well, but there’s an abrupt end to the relationship, and she moves on to Kyle Scheible (Timothée Chalamet), a too-cool-for-school guitarist who enjoys striking rebellious poses. Linking up with him takes her into a richer crowd, and to fit in she not only affects being well-to-do herself but drops Jules from her circle in favor of Jenna (Odeya Rush), the campus mean girl. Needless to say, that does not work out well.

Other things do, however, and like Gerwig, Lady Bird eventually finds her way to New York. She also comes to realize that Marion is no monster, but a woman who has been struggling to make the best of a bad situation for her family, as well as the importance of real friends. The learning curve, moreover, is not one-sided.

As both writer and director, Gerwig handles all these major plot points with incisiveness and skill. She’s helped enormously by an exceptional cast. Ronan is simply inspired here; she might have taken Gerwig as a model in external terms (including, presumably, the red dye job on her hair), but adds to the character a full inner life that becomes almost palpable. Metcalf matches her with a ferociously real turn that ensures her consideration at awards time. Hedges, who is quickly becoming the go-to guy for teens with obstacles to overcome, captures a very different tone from the ones he expressed in “Manchester by the Sea” and “Three Billboards Outside Ebbing, Missouri,” and Chalamet, whose resumé is also expanding rapidly, makes sullen Kyle both attractive and a mite appalling. Feldstein is a delightful newcomer, giving Jules genuine poignancy, and Letts does the same with supportive Larry.

Moving beyond the basic plot, Gerwig adds to the scenario plenty of amusing grace notes. The school scenes are enlivened by the presence of veteran Lois Smith as the genial old nun who oversees the place, and the drama club interludes by that of Stephen McKinley Henderson, as the priest who serves as its sponsor—an overweight, weepy fellow who gets a mite too invested in his work (when he’s abruptly replaced by the school’s football coach, it makes for a hilarious change of approach).

Gerwig also assembled a talented behind-the-scenes crew, who give the picture a professional look that belies what was undoubtedly a modest budget. Chris Jones’ production design and April Napier’s costumes provide a period feel without undue exaggeration, and Sam Levy’s cinematography makes excellent use of the locations in Sacramento and New York. Nick Houy’s crisp editing and Jon Brion’s unassuming score are also positives.

Greta Gerwig has already proven herself one of our most watchable young actresses, adept in both comedy and drama. Now she’s shown that she’s an accomplished writer and skillful director as well. And at least in this case, her own life has provided her with ample inspiration: “Lady Bird” is an exceptional portrait of a fraught mother-daughter relationship, both funny and touching.