There is something very Alice in Wonderland about the work of Jasper Johns, an immense treasure house of games and allusions, seemingly playful and serious at the same time. You can get lost in his world, fall through the rabbit hole only to end up right back on the surface, never quite sure if what is deep can be separated from what is purely fun.

A new exhibition of Johns’s print work at the Phillips Collection is titled “Jasper Johns: Variations on a Theme.” It features about 101 prints made over the course of Johns’s career, from 1960, when he started experimenting with lithography, to virtuoso works he made as recently as a year ago. There’s been no shortage of recent attention to the life and work of the 82-year-old American artist. The National Gallery of Art focused on the seminal decade from 1955 to 1965 in a major Johns exhibition five years ago. The Metropolitan Museum of Art and the Chicago Art Institute hosted an exhibition in 2007-08 devoted entirely to the artist’s focus on the color gray. And President Obama awarded Johns the Presidential Medal of Freedom last year.

But Johns’s work is dense, difficult and rewarding, and it’s hard to imagine it will ever be overexposed. The focus on Johns’s print work doesn’t capture the artist working in a lesser mode or merely duplicating his ideas in another format. Print has been central to Johns’s thinking since he started working with the Universal Limited Art Editions early in his career. ULAE sounds like a publishing house, but in the late 1950s and ’60s it was more like a religious collective, devoted to regenerating the tradition of printmaking by infusing it with an electrical jolt of contemporary artistic talent and experimentation. Invited to work in the form by ULAE’s visionary leader, Tatyana Grosman, Johns threw himself into the details and technique of the process.

The early results on display are tentative and strangely moving. Johns had carved out territory in the fractious New York world of abstract painting in the 1950s by focusing on visual material that lived resolutely in a two-dimensional, symbolic world. His paintings of flags, targets and maps seemed to point to a pop-art sensibility, but they proved a vigorous stimulant to Johns’s painterly tendencies, his love of the physicality of paint and the drama of making it seem to move and dance on the surface of the canvas. A target, merely a collection of concentric circles, was a way of painting something and nothing at the same time, a bit like dummy text that designers use when laying out a page before printing or the rote nonsense speakers use to test a microphone (“how now brown cow.”)

But look at Johns’s early lithograph of a target, and it’s hard not to see a very canny sensibility at work. When he was painting targets, Johns used bands of color to create his iconic image. In this early print, he was thinking in black and white, and the target is radically altered in the process. Johns’s scribbled shading produces something more akin to an eye than a target. Rather than the weightless and uniform clear bands of Johns’s target paintings — which often seem like instruction manual illustrations for how to draw a target — this lithograph is dominated by its dark center, which looks like an iris, an aperture or a portal.

President Obama awarded a Presidential Medal of Freedom to Jasper Johns last year. At right is former president and fellow medal recipient George H.W. Bush. (Bill O'Leary/THE WASHINGTON POST)

As with many other images in the exhibition, you have to know it’s a target to find the target, which reverses the usual thinking about Johns’s work: that his elemental material is so obvious, it disappears. If you can “unsee” the dominating power of the iconic target, the image becomes a fascinating hybrid, fusing the target’s reference to ambition (what we aim for) with the act of seeing.

And so there is an eye staring back at you from the beginning of this exhibition, an apt figure for work that rigorously explores how, if we can briefly interrupt the unconscious act of seeing, the eye works in myriad complicated and dizzying ways. Many prints explore ideas related to mapping, reductionist and appealing surfaces that organize space in congenial ways. Others carefully balance elements (a coffee tin filled with paint brushes, a wood-grain pattern, a background of color crosshatches) in such a way that the eye is uncertain whether to read them “up” or “down,” to inflate the visual code into a fully three-dimensional representation, or dematerialize anything “real” in them and let the image be all jazz and color on the surface.

“Variations on a Theme,” the subtitle of the exhibition, may refer to a macroscopic sense of Johns’s career, which has resolutely focused on what increasingly appears to be a small, private breviary of signs and images, or to the process of printing, in which every reproduction is also a small variation on the original. Johns’s tendency to rework the material thing that produces the print, the stone or plate, emphasized the range of variation possible and the tension between the original and the image it produces.

Variation is best not understood in the old musical sense, the elaborations a composer makes on some basic melody or bass line. Rather, it is a process of continual evolution, leaving in doubt whether one can confidently identify any prototypical theme.

In the later 1960s, Johns started working in the Los Angeles print shop Gemini G.E.L., where he eventually began producing reliefs in lead. Using thin sheets of the malleable but heavy metal and a powerful hydraulic embossing press, Johns created “prints” that look more like printing plates. They are dark and feel archaic, their detail reminiscent of ancient carving rather than modern printing. A 1969 plate, with an embossed and painted piece of paper depicting a slice of bread on the surface has a powerful sense of the platonic ideal to it, a piece of white bread that looks almost edible floating in a dreamlike sea of dark metal. Again, the pop-art sensibility is on the surface, but something more powerful is happening as well. Platonic forms, a powerfully influential philosophical idea about how timeless, perfect ideals of things are antecedent to the messy world of actual things, are sometimes analogized to the process of printing, as if the forms are originals from which a secondary world of prints are made.

Johns’s platonic form of a piece of bread — a very American piece of white bread — is in fact a “print,” a reproduction, just as the philosophical distinction between ideal forms and things inevitably breaks down in a messy logical confusion. And if there’s a comment on the world in his choice of a tasteless, ubiquitous and nutritionally nugatory slice of bread, it may have something to do with the way that definitions limit us. Because it is everywhere, easily reproduced in almost identical form, the American slice of white bread is the definition of bread for many people. The thing that is reproduced becomes the ideal, and no other form is adequate.

The exhibition is organized roughly chronologically, and as Johns ages, his language becomes more enigmatic and less purely conceptual. If there is a mysterious theme hidden underneath all these variations, perhaps it is purely personal. One has the occasional sense that Johns’s entire life may be an exceptionally rigorous form of self-discipline, a game of clues and codes that someone may someday unravel into a biographical narrative.

But he tells us not to look. “Avoid the idea of a puzzle which should be solved,” Johns once said of a work he made in 1983. That seems to suggest the viewer should remain passive in front of the work, succumb to the idea that there is no puzzle there. But Johns’s words are ambiguous (and the missing comma in the text makes them more so): Perhaps there is indeed a puzzle, just not one that can be solved.

Taken that way, the “theme and variations” in Johns’s career becomes a strangely heroic and Quixotic quest, an endless pursuit of a theme that may not actually exist.

In a 2010 print, “Fragment of a Letter,” the artist uses images of a hand making sign language almost as background material. It seems to encapsulate Johns’s ambition, not just to have fun with codes and signs by translating them from one medium to another, but to make a picture of communication.

It isn’t possible. The artist can depict many things, but depicting how we see isn’t among them. Yet that often seems to be Johns’s goal, a life-long series of feints at an elusive image of visual codes actually at work, doing their job, communicating ideas about the world. It is Sisyphean work, and after studying decades of it, it’s worth stepping back into the exhibition at the beginning point in 1960.

The target that is an eye will haunt you.

Jasper Johns:Variations on a Theme

is on view Saturday to Sept. 9 at the Phillips Collection, 1600 21st St. NW. 202-387-2151. .