Part of the charm of “An Education,” a bittersweet coming of age story based on a brief memoir by Lynn Barber, is how much we know what its main character does not. Jenny (an incandescent Carey Mulligan) is a teenager in 1961 London, over-protected by her overly-cautious and conventional parents and eager to be independent and to have adventures. She is used to being the smartest one in the class and so even more than most teenagers, she is convinced that she understands many important things her parents cannot possibly comprehend. She is eager to grow up, to seem sophisticated, to be sophisticated. She is innocent, filled with potential, willing to be taught — and she has no idea how powerfully attractive those qualities are to a predatory older man.

But we know that, and when David (Peter Sarsgaard) rescues Jenny and her cello from a rainstorm by giving her a ride home, we know she will confuse urbanity with wisdom, that she will think that because he lies on her behalf he will not lie to her. But the most important thing we know is that like Jenny, London is also on the brink of enormous changes. We know that a world of opportunities she could never imagine will open up to her. Unlike Jenny, we know she is going to be fine. After all, we know she went on to tell her story, in itself a triumph over whatever went wrong and whatever she lost.

Danish director Lone Scherfig perfectly captures London just as it is about to move from the drab, stiff-upper-lip, world of post-WWII deprivation to the brash and explosive era of mods and rockers, Carnaby Street and the Beatles, Twiggy, “The Avengers,” and Joe Orton. Part of what makes David so exciting is that Jenny believes that the only options available to her are teacher and housewife and the only examples of both she has seen appear dull and unrewarding. David gives her a glimpse of a life that is never dull. It is always shopping and parties and travel, pretty clothes and lovely restaurants. If in order to have all of that she must lie to her parents and defy her teachers, that makes it all the more exciting. It binds her to him even more, creating a set of rules that is just for them.

That is how it seems, anyway. The education referred to in the movie title tells us that she will learn some difficult lessons. But its conclusion reminds Jenny and us that it is only the end of her beginning. She thought meeting David was the beginning of her future; she learns that the real beginning only came afterward.

The screenplay by Nick Hornby (“High Fidelity,” “About a Boy”) is sympathetic but insightful, skillful in sketching in each of the characters. Sarsgaard also makes David more than a predator. Jenny is not just smarter than he is; she is stronger, too. As Jenny goes from school girl to dressed-up doll to the beginning of adulthood, from the make-it-do, wear-it-out modesty of her home to Paris hot spots, Production designer Andrew McAlpine and costume designer Odile Dicks-Mireaux show exquisite sensitivity in giving Jenny a look that tells the story. Every performance is a gem: Alfred Molina, proud but fearful as Jenny’s father, Emma Thompson, starchy as the headmistress, and Olivia Williams, a teacher who wants more for Jenny than she wants for herself (it must have been quite a challenge for hair and make-up to turn Williams into such a dowdy character). Rosamund Pike is utterly charming as a dim but kind-hearted party girl. And Carey Mulligan, in a star-making turn, makes this into one of the best films of the year.