Maurizio Pollini has been playing before the public for more than 40 years. In the Maurizio Pollini Edition, a new Deutsche Grammophon 13-CD compilation of his recordings (mostly from the 1970s), there’s a live performance of Chopin’s First Piano Concerto from the 1960 International Chopin Competition in Warsaw, when Pollini was only 18. The sound is muddy, the conducting nothing special. But there’s an extraordinary sweetness in the playing and every now and then — already — the anticipation of that miraculous Pollini sound: the uncanny definition of every note, no matter how fast it’s going by, no matter how many other notes are also rushing past, that brilliant gleam that some critics have called cold but that seems like controlled white heat to his admirers, and the shapeliness of the phrasing, the sense of both moment and movement, of direction, of continuity, that everything is connected, coming from somewhere and heading somewhere.

The set also brings home in the most graphic way the extraordinary range of Pollini’s musical interests. There’s no Bach (the one area in which he profoundly differs from Glenn Gould), no Baroque music at all — the earliest composer represented is Mozart. But then there’s a direct line from Mozart to Beethoven (six sonatas, three concertos) to powerful, radiant Schumann, eloquent Schubert, magisterial, moving Brahms, unmelodramatic Liszt, brilliant yet unshowy Chopin, scintillating, witty Debussy. Then — zoom! — we’re in the 20th century.

Pollini was the second of the only two major pianists to record the complete solo piano music of Schoenberg, including the Piano Concerto (Glenn Gould beat him by a decade). There are Webern’s Variations for Piano (in a ravishing performance), Stravinsky’s dazzling Three Movements from Petrushka, two breathtaking Bartók concertos (with the Chicago Symphony Orchestra under his friend Claudio Abbado), and then — zoom again! — music by some of the most radical of the next generation of moderns: Pierre Boulez’s exhilarating and still challenging, even bewildering, Sonata No. 2 (composed in 1948, when he was only 23), and pieces composed for this so-called conservative pianist by his favorite avant-garde Italian compatriots, Giacomo Manzoni and Luigi Nono. One Nono piece, Como una ola de fuerza y luz ("Like a Wave of Strength and Light"), from 1972, has (I’ll go out on a limb) the most elegant pounding of cluster chords on record; the other, . . . sofferte onde serene . . . ("serene waves suffered"), for piano and tape, Pollini imbues with a misty, glistening beauty. No Russians. No Americans! But by no stretch of the imagination could you call his range narrow.

Two years ago, in New York, I heard him participate in a brand new piece by another Italian composer, Salvatore Sciarrino, with the London Symphony Orchestra conducted by Pierre Boulez — though he hasn’t, to my knowledge, played any contemporary music in Boston. Or any early music, though among the nearly 30 programs in his "Perspectives: Maurizio Pollini" series, at Carnegie Hall, there’s been music that went back to the 14th century.

The Mozart on the Maurizio Pollini Edition is the most heavenly of the master’s mature piano concertos, No. 23 in A, K.488. Karl Böhm conducts the Vienna Philharmonic, and under the spell of Pollini’s elegance, this conductor has left behind his often heavy approach. There is gravity without weightiness, depth of feeling without sentimentality — never any milking for pathos. Of course, there’s the glittering touch (amazing how many of today’s superstar pianists make a sound that has no particular color or identity or inherent vibrancy), but Pollini combines that touch, and a rhythmic buoyancy that in his best performances never lapses into automatic pilot, with an absolutely unshakable, inarguable sense of architecture. Not only do you hear every note, you hear the structural and emotional import of every note — and then you can’t wait for the next one.

The transparency of Pollini’s touch is ideal for Mozart. But it’s also perfect for Beethoven. There’s a magical, floating bell-like phrase in the first movement of the Emperor Concerto that returns at the end of the movement as a kind of vision of Heaven, and Pollini practically makes it glow. In a live 1988 performance of the Waldstein Sonata, he delivers the famous opening thunder and lightning with a mysterious muffled intensity. But what’s even more remarkable is the transition from the questioning slow movement to the exhilarating finale. Some pianists make this transition too quickly and create a kind of pumped-up excitement. Beethoven’s marking is Allegretto moderato; some pianists observe it too literally and the transition drags. Pollini takes it as marked, but this time, in Beethoven’s turn from inward contemplation outward to the world, he shows us Beethoven opening his eyes, gradually but deeply taking in the vast expanses of the world’s loveliness. This deeply considered pacing bursts into a propulsive Prestissimo that brings this performance to an overwhelming climax.

One piece it’s fascinating to compare with another famous performance: the last-movement Waltz from Schoenberg’s Five Piano Pieces, Opus 23, his very first music to employ fully the 12-tone system. Pollini plays it as a real waltz, in the tradition of Brahms and all the Strausses. It’s flowing, gemütlich, lilting, yet its harmonies are also something new in the world. Pollini lets you hear the continuity not only within this short piece of music but also with its history, the past out of which it has emerged.

Glenn Gould was playing Schoenberg in the early 1950s, and he was devoted to that composer; he performed and recorded not only the solo piano pieces and the concerto but also the vocal pieces with piano accompaniment. Compared with Pollini’s version, his 1965 recording of the Five Piano Pieces sounds as if it had come from a different century — a newer century. It’s disjunctive, angular, even jagged — nothing if not modern. You can hear the shadowy waltz in the distance, but this isn’t music you could dance to — at least, not waltz to. It’s like a Kandinsky abstraction, exploding on the canvas. Pollini is more like a Cézanne watercolor. There’s an image you can read. It may not be quite as much fun as Gould’s version, as crackling, but it’s more knowing, more insinuating, more European, and more beautiful.

Pollini, however, isn’t always "on." The one disc that leaves me disappointed is the one with the two late Beethoven sonatas (from 1977), the impossible Hammerklavier and the last sonata, Opus 111, where I think it’s the sheer facility of Pollini’s playing that rather undercuts the very struggle with form and articulation that Beethoven seems to be grappling with. Or maybe his timing is just a little off. At any rate, his performances of these two profoundly moving works don’t move me the way the recordings by Artur Schnabel, or Annie Fischer, or Russell Sherman do.

Pollini often seems shy in front of an audience. I’ve heard concerts that have taken him the entire first half to warm up, though on this CD set, the live performances (the Waldstein, the Schumann Piano Concerto under Herbert von Karajan) reveal his capacity for leaving his inhibitions behind.

His most recent FleetBoston Celebrity Series recital (his 13th) was, like his 1997 Symphony Hall program, devoted to Chopin and Debussy, and it began auspiciously. The repeated descending steps that open the Chopin F-minor Fantasy (leading down to what abyss?) had a dark, visionary seductiveness. But the rest of the Fantasy had no real point of view. It seemed clotted, over-pedaled, too heavy on the left hand, and consistently a hair too fast. It didn’t breathe. The Barcarolle, though it built tremendous steam, was less a song for a gondolier than for a speedboat driver, cutting through the waves rather than being subtly shifted by them. There was little variety of color or dynamics. And where was Pollini’s magical hush? In 1997, the Berceuse ("Lullaby"), like the one on the CD set, was as tender as a whisper; this time, his emphasis on Chopin’s strange harmonies would have kept the baby awake. In the Third Scherzo he played in 1997, he reveled in the contrast between the chorale of low-lying chords and the specks of high notes floating down like confetti; this time, the high notes were too loud — there was no dynamic differentiation. He wasn’t playing his usual piano, so maybe he misjudged his own touch.

Almost everything else suffered from these same shortcomings. Not a note was out of place, but there wasn’t much getting across besides the notes. In 1997, Pollini played Book One of Debussy’s Préludes; this time it was Book Two, and he played all 12 without pause. It was a phenomenal technical achievement, with brilliant moments: the lightning flashes cutting through the fog of Brouillards; the cakewalk and peremptory final chord of General Lavine — eccentric; the joke of "God Save Our Gracious King" infiltrating Debussy’s homage to Dickens’s Mr. Pickwick. But the most emotional moment in the concert came in the piece requiring the most fireworks: the final Prélude, Feux d’artifice. The quietly spinning pinwheel with notes flying off like sparks, the roller-coaster glissandos, the explosive climaxes, the rumbling aftershocks, even the hint of a triumphant Marseillaise — every note told. Here, finally, was the Pollini of one’s dreams, centered, richly imaginative — and enthralling.

The audience didn’t want to let him go. Giving repeated shrugs, he seemed happily resigned to keep going. Maybe he needed to. He played five Chopin encores, beginning with the First Ballade (which was part of his 1997 program here — and which evidently so thoroughly mesmerized someone down front that she remained standing for the entire piece, though for me it didn’t "sing"), then two Préludes (a funereal Raindrop and the powerful last Prélude, in D minor), and the Revolutionary Étude — as if sensing that bravura, the heavy artillery, was what was working best. But it was only the last encore, one he also played in 1997, the touching, indrawn D-flat Nocturne Opus 27 No. 2, in which his fullest imagination seemed reactivated.

What a peculiar, frustrating, profoundly satisfying, unpredictable, erratic genius. How could he not be one of the world’s most cherishable artists? We’re lucky to hear him, even on one of his off days.