If you’ll recall from high school art history, James McNeill Whistler was that one artist who painted that one unassuming portrait of his strict-looking mother in profile. But recall also that “Whistler’s Mother” is officially titled “Arrangement in Grey and Black No. 1,” and the painting evolves, becoming less a portrait per se than a radical study of color and composition, of how to create harmony from shades of gray. This artistic evolution within a painting is writ large over the course of Whistler’s career, as traced in “Whistler in Paris, London, and Venice,” which runs until July 19 at the Yale University Art Gallery.

“Whistler in Paris” is, in short, a biographical exhibition. It isn’t merely concerned with giving us a visual showcase of the artist’s work — though his etchings, on which the exhibition focuses almost exclusively, are consistently breathtaking and stand up perfectly well on purely aesthetic terms. Rather, the collection presents Whistler’s maturing aesthetic considerations as a vehicle for understanding his life, both intellectual and personal. (So much for his advocacy of “art for art’s sake.”) As such, it follows a straightforward chronology, grouped into three early sets of etchings: the French, Thames and Venice Sets, whose titles reflect the physical and cultural locales in which Whistler produced them.

There’s a reason why the exhibition is called “Whistler in Paris, London, and Venice,” and not simply something like “Whistler” — the works showcase, specifically, Whistler the lifelong expatriate, who left for Paris at age 21 and never returned to America. Despite his persistent outsider status, however, he displayed an impressive facility for adaptation, associating himself with key figures in various intellectual movements and absorbing a variety of influences. One of his lithographs, for instance, depicts a vast gallery in the Louvre, in which he would study the techniques of the Old Masters.

Similarly, Whistler managed to embed himself quite literally into his foreign surroundings, an ability that lends his etchings greater intimacy. For all his dandyism and refinement, the artist demonstrated a deep interest in the seamier aspects of his surroundings — a recurring theme in all three sets. The best etchings of the “French Set,” for instance, depict working-class individuals — an old woman with rags, a mustard seller, rag pickers. Later, Whistler eschewed the monuments and tourist traps of Venice for what he called the “Venice in Venice,” hopping into a gondola and exploring the city’s back canals. Hence, in one etching, we see a cloth-dyer from water level.

The most visually cohesive set comes between Paris and Venice, the “Thames Set.” Although it was in London that Whistler began to achieve concrete success as an artist, the world depicted in his etchings of the Thames expresses none of that newfound glamour. But the beauty of these quiet industrial waterscapes is grounded in their realism, and they feel truer to the inner life of the city. In time, Whistler somehow figures out how to convey that using less and less; the final etching in the set, “Chelsea Bridge and Church,” has a sparser, more distilled quality. It’s here that you can see his focus evolve from pure representation to a greater consideration of artistic elements in themselves, like line and shape. Nearby is one of his “Nocturne” paintings, a hazy view of the Thames that takes its name from a musical form. Whistler’s quoted as saying: “Nature contains the elements of color and form of all pictures — as the keyboard contains the notes of all music,” and it is up to the artist, and the musician, to arrange these elements and “bring forth from chaos, glorious harmony.” Recall Whistler’s mother.

These sets are well complemented by other parts of the exhibition, including presentations on the etching process, which give us a better appreciation of Whistler’s technical mastery, as well as works by his pupils and contemporaries, which contextualize him as an artist. In particular, “Whistler in Paris” explores his influence on American contemporaries; an oil painting of a Brooklyn harbor by William Merritt Chase brings to mind Whistler’s Thames. Thus, even if Whistler never returned to America, his artistic vision did. In a fascinating bonus section, scratched-out etchings from a “fourth” set, the “Cancelled Set,” can be viewed. These are accompanied by wall text relating Whistler’s bankruptcy and the decline of his reputation before the turning point that was Venice.

“Whistler” is comprehensive in its presentation of the artist’s life, his failures and successes, and all the paradoxes of his character. Here is a self-dubbed “mercurial butterfly,” an American expat, an aggressive self-marketer, yet a champion of decidedly non-commercial subject matter in his work. But, as in his art, in the blacks and whites of “Whistler’s Mother,” he pulls off these contrasts. In glimpses of the Thames, and in a gondola in Venice, from all the chaos of life, Whistler gives us a strange harmony.