The painter greets us, naked. She holds a gun to her own head, and aims another at her spectators. Maria Lassnig, approaching 90, might be trying to tell us something. You or Me is the title of this self-portrait, painted in 2005 and the first thing you see in her exhibition at the Serpentine Gallery in London. As well as an introduction, the painting is a test: bolt and run, or stay and face the consequences. I plunged right in.  Born in Austria in 1919, Maria Lassnig is little known in this country. This exhibition of her awkward, confrontational, strange and tender paintings is her first show in a public space in Britain. Lassnig's works have sometimes been regarded as pathological caricatures. In Austria, one might almost take this as a compliment, or a sign of her authenticity. Lassnig, on the other hand, insists that her art is completely rational.  I sat with her among her paintings, some still being positioned on the walls, and she told me she often begins with no idea in mind at all. Nevertheless, there are constant themes. War, love, the battle of the sexes, the subjective experience of the body. Most of all, the body: dressed, undressed, veiled in plastic, malleable, devilish, sexual, grotesque. In one recent painting, a man pulls himself upwards on a gymnast's rings - "I hate sport," Lassnig remarks - and in another, someone gets tangled in plastic sheeting. There's comedy here, but it never comes unalloyed.  Sometimes Lassnig paints herself as an alien, or blindfolded and with a saucepan on her head (a sort of blind Liberty, perhaps, leading no one but herself). There is a painting of her cuddling a teddy bear; green-skinned and with a terrified look on her face, the artist takes solace in the bear's comfortingly blank expression. She also paints herself painting herself - except that the painter's head has been severed, and the twin whose nipple she paints has both the body of a baby and an elderly head.  A wilful individualist of great dignity and extreme candour, Lassnig studied in Vienna during the second world war. The library shelves had been cleared of corrupting influences, and she painted everything brown. She was told she painted like Rembrandt. Seeing expressionism and surrealism after the war was intoxicating. In the 1950s Lassnig went to Paris, where she met the capo of surrealism, André Breton, and where her work was admired by Yves Klein. Later, she travelled to New York. She says that in the 1970s no one there much cared for her paintings: they thought they were deformed. "Americans are so simple-minded," she says.  While in the US she made a number of animated films, in which she was the wry and stoical heroine - ambitious, disappointed in love, confused about relationships, bodies and art. A few weeks ago I saw some of these short films in the brilliant exhibition Wack!: Art and the Feminist Revolution, at PS1 in New York, where they struck a rare light-hearted note. Lassnig also took an interest in performance art, and admired in particular the work of Dan Graham. In 1980, she was appointed professor at the Academy of Applied Arts in Vienna, the first female professor in a German-speaking country. You don't take on a role like that just to be a figurehead, and Lassnig taught until well into her 70s.  Lassnig's art, which shares traits with expressionism, reminds me intermittently of the American portraitist Alice Neel, and also of one grasping for connections with much younger generations of artists. Martin Kippenberger was a fan; Paul McCarthy collects her paintings and has contributed an essay to the catalogue for this show, a text purposely disjointed and ripe with images of amputations, bodies turned inside out and impossible actions: "The finger goes in the mouth up through the nostril cavity and out the eye-socket ... your arm is over here, your head is on the shelf, and your torso is on the chair."  McCarthy's disturbing psycho-sexual manipulations echo what Lassnig calls her "Body-awareness paintings", and her more recent "Drastic" paintings. These strands of her art are developed from the sensations one has of one's own body, mapped and felt from the inside, rather than from observation or through anatomy and what the mind already knows. In the past, she painted bodies as dumplings, bodies as sacks of potatoes. By contrast, her new paintings are all bulge and spike, thrust and recoil. These bodies are malleable plastic forms, rapidly executed, extruded and abbreviated against cursory or even bare backgrounds. At times, they remind me of Ren and Stimpy cartoons. Bodies are reduced to penile shafts. The mouths are in the wrong places. Limbs wither or bloat, noses become porcine snouts. Lassnig is in there, too, her own physiognomy morphing and struggling. These paintings have a weird filial relationship to Carroll Dunham, to Nicola Tyson, to the strange anthropomorphic plumbing in the early work of sculptor Eva Hesse.  There is also tenderness, affection and romance: a young couple lean together like dancers, and hold one another in a loving embrace. Above them, pigeons coo on a wire. There are crows up there, too, perhaps awaiting the end of love's young dream. Another couple are veiled in polythene, locking eyes through the plastic.  Lassnig says she first painted plastic when she saw supermarket-wrapped fruit and vegetables in America, and thought how bizarre it was. In the beautiful and frightening The Illegitimate Bride, a naked woman approaches, backlit, her face in shadow, her only clothing a voluminous, stiff bridal veil of plastic. One sagging breast glows in filtered light. The paint handling goes from the crude to the delicate, and the colour and touch are oddly reminiscent of the late David Bomberg, but without the dreary earnestness. It is marvellously inventive, rich and awful.  I told Lassnig I found a strange, exhilarating mix of tenderness and violence in her art. Careful with her words, she said: "I am interested in painting the finer feelings," which took me aback. But then she asked, "Have you seen in there?", pointing through a doorway. In there are several paintings of a fat, naked, middle-aged man. In one he's kneeling over what appears to be an inflatable toy. No, Lassnig tells me, not a toy, a girl, and the painting is about child molestation. The girl is pink, formless somehow, and she has no mouth - no voice, in other words; one dumb little button eye looks skyward while the man peers down at her. In another painting, the fat guy supports the horizontal body of an adolescent waif on the palms of his hands. They are the hands of a butcher, toying with a slab of steak. The girl's high-heeled shoes are drawn with a light, dainty touch. The expression on his face is neutral, as though he were far away. Hers is, too. Presumably he's locked in his fantasy world, she in wishing it were over, wishing she were dead.  Lassnig often uses her neighbours in rural Carinthia as her models. These include her local priest and churchwardens. Some of these models are happy to undress for her, or to pose in the bath, or on the bidet, or naked in her white studio. A large, naked woman sits behind a display of cakes. A woman draped in plastic, lit from below by artificial light, is as luminous and weird as Joseph Wright of Derby's Experiment on a Bird in the Air Pump. Lassnig's paintings are experiments, mostly in seeing how far you can go. She told the German critic Jörg Heiser that embarrassment is a challenge, and that she seeks out the uncomfortable.  In one very odd painting, a humanoid figure crouches on the ground. Beside it a grotesque head grows from a stalk, sticking its tongue out. Nearby stands another oddly bird-like figure. The painting is called Photography Against Painting, but I'm not sure which is which in this peculiar composition. Photography is lazy, Lassnig thinks. Tell that to Gerhard Richter, I suggest, to Francis Bacon, even to Degas. They all used photography.  She gives me one of those looks. She is cross with Bacon for deriving his figures from photographs, and has mentioned to one interviewer that Bacon was "like a good boy" for painting in the backgrounds of his paintings so diligently. Much of the time, Lassnig leaves them out. If she has anticipated the work of younger artists, Lassnig says that these days she doesn't pay much attention to what's going on in the art world. She just works.  If anything, Lassnig's art gets more confrontational and direct as time goes on. There is no hesitation and no fudging. There really isn't time for her to be anything other than straightforward. Yet the paintings also contain intractable ambiguities. They keep us looking, while she looks back, one gun to her temple, the other pointed our way. Bang.  · Maria Lassnig is at the Serpentine Gallery, London W2, tomorrow until June 8. Details: 020-7402 6075. serpentinegallery.org
At nearly 90, the painter Maria Lassnig is producing the most confrontational work of her life. She talks to Adrian Searle