Legend has it that when Picasso visited Paul Klee (1879-1940) in Bern in 1937, he professed: “I am the master of the large. You are the master of the small.” Picasso, who remained a representational artist, would have been more correct if he had said to Klee (an abstract painter): “I am the master of the outer realm – the world of appearances.You are the master of the inner realm – the mystic world of dreams.” For although it is true that Klee worked on a small scale (rarely do his pictures extend larger than 4 feet in any direction), no other artist has so thoroughly investigated the actions of nature and the inwardness of man.

A wonderful, fantastical exhibition, “Klee and America,” opens today at Neue Galerie. Comprising more than 60 paintings, drawings, and watercolors from American public and private collections, it is a garden of earthly and other delights. An encapsulation of the artist’s reception in the United States, it represents the fullness and richness of Klee’s investigations.

Klee was not only a visual artist: He was also a poet, natural scientist, and concert violinist. His broad interests are reflected in the astonishing range and comprehensiveness of his pictures – which can resemble everything from aquariums to stone carvings to stained glass to textiles. They move fluidly between isms, periods, mediums, and styles; literally, between realms and planes of existence. He delved into everything from Surrealism to Romanticism, from the Simultaneity of the Delaunays to Mondrian’s right angle and flat plane. He explored children’s art and Primitive art, as well as botany, geology, and psychology. Klee’s Bauhaus teaching notebooks, compiled posthumously into a two-volume tome titled “The Thinking Eye” and “The Nature of Nature,” have been compared to Leonardo’s notebooks during the Renaissance.

Here in New York we can regularly see small Klee shows culled from the extensive Berggruen Collection at the Metropolitan Museum of Art. Because Klee was so popular in America during the 1930s and 1940s, there is no real shortage, relatively speaking, of his works in public collections. Still, not since MoMA’s 1987 Klee retrospective have so many of his masterpieces been brought together – and lovingly so.

“Klee and America,” arranged roughly chronologically, is curated by Josef Helfenstein, the director of the Menil Collection and the editor of the “Klee Catalogue Raisonne.” It will travel on, in much larger form, to the Phillips and Menil collections in Washington, D.C., and Houston, respectively.

Mr. Helfenstein is intensely familiar with Klee’s more than 9,000 works – and he has not only vision, but also an eye. He has selected a choice, varied grouping of the artist’s pictures for the exhibition, and he has installed them beautifully. Many of the show’s works from the collections of the Phillips, the Menil, the Met, the Guggenheim, and MoMA – “Red Balloon” (1922), “Youth Actor’s Mask” (1924), “In the Current Six Weirs” (1929), “Arabian Song” (1932), and “Printed Sheet With Picture” (1937) – will be familiar to people who frequent those museums’ Modern art galleries.

Judging from the catalog, other masterpieces – “Fish Magic” (1925), “Still Life (Pots, Fruit, Easter Egg, Curtains, Etc.)” (1927), “Young Plantation” (1929), “W=Consecrated Child” (1935), “New Harmony” (1936), and “The Way to the Citadel (Picture of a City)” (1937) – did not make the cut in New York. And a number of key pieces, such as “Night Feast” (1921), “Around the Fish” (1926), and “Fire in the Evening” (1929), are missing from the exhibition. Still, the show, which is filled with surprises, does not disappoint.

Mr. Helfenstein has rightly opted not to include the oft-exhibited early prints and drawings that belong in a retrospective but not in a small show such as this. The survey begins with a dense, Cubist-inspired watercolor, “When God Considered the Creation of the Plants” (1913). In this picture, Klee is already moving beyond Synthetic Cubism into a deeper realm where a strict geometry of rectangles sprouts, unfolds, and transforms into living, wild vegetation.

The show then moves into the groundbreaking watercolors inspired by the Delaunays. These works were made after his visit to Tunisia in 1914. We see two vibrant yet muted works from private collections,”Yellow House” (1915) and “Tunisian Gardens” (1919), in which their stained-glass light seems to be filtered through desert sand.

From here, we leap into Klee’s mature work of the 1920s and 1930s. “Girl With Doll’s Pram” (1923), a dreamy gray fantasy of make-believe, is a portrait of a girl pushing a toy stroller. Some of her features are surreal and grossly oversize: The girl’s hair billows like a ship’s sails and carries her arrow-like eyes, which, like searchlights, are wide open. Her large breasts, like overinflated balloons, are alert, rising, and at attention.

In the same gallery is “Flowers in the Night” (1930), a dark, cool, blue-green watercolor that evokes gestation, underwater views, and nighttime mischief. “Collection of Figurines” (1926), a frenetic oil painting of puppets or shop window mannequins, occasionally breaks into parts, suggesting a freaky reconfiguration of body parts.”Negroid Beauty (Precision)”(1927) is a rather direct ink portrait not only of Josephine Baker but also of the entire streamlined decade of Art Deco.

The second gallery really takes off.Among its two dozen works is “The Village Carnival” (1926), a child’s sanguine fantasy or nighttime journey. Created with a scratchboard technique in which blood reds seep through blackness, the images of houses, a child with a dog, planets, stars, and mystical beings all loom forward and float in the darkness. Sharing wall space with “The Village Carnival” are the works “Abstract Trio”(1923), a portrait of three dancing abstract figures, and “Colorful Meal” (1928), a black ground into which the whole universe – from house to telephone to fork to cosmos – has been embedded as an abstract still life. Also present is “Meganthemum” (1927), a typical Klee hybrid. Like a bunch of whirligigs, the monumental plant – animal/mountain/figure/flower – is held within its red ground, as it spins, frightens, and unfolds like origami.

In the last gallery are the surprising abstract heads “Lion Man” (1934), a fiery watercolor portrait,and “Monument Under Construction” (1929), a watercolor on plaster that, reminiscent of the gaze of the Sphinx, is as rock-solid as it is ephemeral. In the puzzle-like “The Man of Confusion” (1939), a hot-pink, red, and orange field filled with body parts or pieces of a landscape, almost every form in the picture is amorphous.Both floating and embedded in the ground, the forms shift the picture from abstract interior to still life; from toy chest to womb; from artist’s studio to child’s imagination.

Paul Klee is an artist as important to our era as Giotto and Leonardo were to the Renaissance. Though he never set foot on American soil, he continues to be extremely influential here and abroad. But he is often belittled and misunderstood. Because his explorations are so varied, rich, and comprehensive, his influence can be tied to almost every art movement, good and bad, of the last 100 years.

Klee’s heroic emersion into the well of creation, and the riches he found there, have yet to be fully understood or implemented. If there is anything suspect about “Klee and America,” it is in some of the catalog essays. In their emphasis on Klee as a father of Dada and Surrealism, the essays attempt a tidy historical game of connect the dots from Klee to Duchamp, de Kooning, and Rauschenberg – artists who willingly turned their backs on Klee. His poetry and genius then, tremendously desiccated, become merely a stepping-stone on the journey from Romanticism to Dada to Pop art, rather than what it continues to be for many artists – the bedrock and life spring of the Modern Renaissance.

Until May 22 (1048 Fifth Avenue at 86th Street, 212-628-6200).

lesplund@nysun.com