When the 12-year-old prodigy Franz Liszt gave his first public performance in Paris in February 1824, two months after his arrival in the city, the audience hailed him as “Mozart incarnate.” Not since Mozart, who had died 33 years earlier, had Europe seen such a prodigious talent. From earliest days, Liszt — pianist, composer, superstar — was marked out to command the Romantic century. He lived and worked with a fire the equal of any of his peers, then went many of them one better by living to 75 and a quiet, Catholic old age.

“Liszt in Paris: Enduring Encounters,” now at the Morgan Library and Museum, tells of Liszt’s years in Paris in the 1820s and 1830s. He was born in what is now Raiding, Austria, but was in 1811 part of the Kingdom of Hungary. Though he would play up his Hungarian origin (for example, by composing his famous “Hungarian Rhapsodies”), he was a native German speaker and, though multilingual, never quite got the hang of Magyar.

He began his concert career at the age of 9. In 1822 he was in Vienna, studying with Beethoven’s pupil Carl Czerny. In Vienna, legend has it, Beethoven kissed young Franz on the forehead. Whether or not Beethoven bestowed this “kiss of consecration” takes up inordinate space in the Liszt scholarship.

The exhibit’s first section is titled “The Prodigy.” Liszt studied composition as well as piano. The Morgan shows the cover of the first English edition of “Seven Brilliant Variations, for the Piano Forte, to a Theme of Rossini, op. 2,” dated as circa 1825, by “Francis Liszt.” (At least they didn’t call him Frank.) Such was his progress that when in 1824 Anton Diabelli invited several prominent composers — including Czerny, Johann Hummel, and Franz Schubert — to each write a variation on one of his waltz themes, he included the 13-year-old Liszt.

The second section, “Chopin,” tells of Liszt’s relationship with the Polish composer-pianist, which was cordial but not close. Chopin arrived in Paris in 1831 as a refugee from Poland. The two piano titans represented two different approaches to the instrument — in fact, different instruments. Chopin played a Pleyel piano, known for its delicate, soft sound. Liszt played an Erard, a heavier piano, with faster action. Many of Liszt’s piano innovations required an Erard.

The exhibit, which draws almost exclusively from the Morgan’s matchless collections, features autograph manuscripts of Chopin’s “Variations sur le Thème de Mozart,” 1827, and “Étude,” 1832. There is also an 1853 edition of George Sand’s novel “Lucrezia Floriani,” a thinly veiled account of her relationship with Chopin, whom she first met at a party given by Liszt in 1836. Liszt appears in the novel as “Salvatore.” (He later appeared as “Klesmer” in George Eliot’s “Daniel Deronda.”)

The Morgan has two listening stations set up where you can listen to works that appear throughout the show.

The section “Berlioz” chronicles Liszt’s friendship with Hector Berlioz. Liszt attended the first performance (December 1830) of “Symphonie Fantastique” in the company of its composer. The two men enjoyed a warm friendship until much later, when they drifted apart: Berlioz was crazy about neither Liszt’s orchestral compositions nor his support of Wagner. In this section, we find an autograph letter from Berlioz to Humbert Ferrand informing him that Liszt had just made a piano arrangement of the entire “Symphonie.”

The section on “Paganini” relates how Liszt first heard the virtuoso violinist Nicolò Paganini in Paris, in 1832, at a sold-out concert in the midst of a cholera epidemic. Liszt felt as though he’d been struck by lightning. He began the improbable task of translating Paganini’s violin virtuosities to the piano, abounding in rapid scales and repeated-note passages requiring great speed and stamina — and the speed, responsiveness, and dynamic range of the big Erard piano. At the listening station, you can hear Paganini’s “Grande fantaisie de bravoure sur La Clochette” as translated to piano by Liszt.

Finally comes Wagner, who does not really belong to the Paris part of Liszt’s story, but no matter. Wagner was the second husband of Liszt’s daughter Cosima. And Liszt was one of Wagner’s great champions. (Even so, he was disappointed with Cosima for divorcing his former student Hans von Bülow.) Liszt gave Wagner financial assistance and helped him to flee Dresden after the 1849 uprising. The exhibit shows the first edition of the libretto of “Lohengrin: Romantische Oper in drei Akten,” 1850, of which Liszt had conducted the premiere in Weimar.

Liszt outlived his son-in-law by three years. (Wagner was only two years younger than Liszt.) The Morgan shows the autograph manuscript of “Am Grabe Richard Wagners,” which Liszt wrote in 1883 in commemoration of the deceased Wagner.

A beautiful 1837 map of Paris is mounted behind glass on which stickers note the residences between 1823 and 1856 of Liszt (five of them), Berlioz (eight), and Chopin (eight), and concert venues, including Salle Pleyel and Salle Erard.

The map is all that gives a sense of what the city outside the drawing rooms and concert halls was like. Liszt’s Paris was the Paris of “Cousin Bette,” of “Les Enfants du paradis,” of “La Bohème” — a ceaselessly creative Paris that existed in the fetid, pestilential conditions that prevailed in that city before Emperor Napoleon III transformed Paris into the “City of Light.” Some of that background would have been a nice addition to what is otherwise a beautifully orchestrated exhibit with many treasures.

Until November 16 (225 Madison Ave., between 36th and 37th streets, 212-685-0008).