Lucian Freud painted strange, uneasy, figures, from first to last. Maybe they were uneasy because he was painting them. There was as much violence as tenderness in his stare, and in the ways he devised to paint.
This tremendous show tracks Freud's inquisitiveness and inventiveness, his constant returns to the mystery of presence. Almost everything Freud did was a portrait of a situation or a confrontation as much as it was a body in a room, whether the body belonged to a lover, a daughter, the artist's mother, a baron, a bank robber or the Queen.
Freud was 18 in 1940 when he painted his art college tutor Cedric Morris , the earliest work in this large, though far from complete exhibition, planned in close co-operation with the artist himself during the last five years of his life.
Freud's final painting, of his pet dog and his studio assistant David Dawson, was left unfinished on the easel when Freud died last year at 88. Its incompleteness is extremely affecting.
The first of these two paintings is small, querulous and faux-naive (though it is hard to imagine Freud naive at any stage in his life), the last full of eccentric impetuosities: Dawson looks up; Freud's eye circles like a bird of prey, quartering its subject from above. The painting runs the gamut from sketchy indications of what might have been, to revised and much reworked detail. Dawson's head is an encrusted eruption of granular pustules of paint. I churn too, as I look at it.
In his very late works Freud seems to have got fixated on certain details. There is an enormous, disjunctive, variety in Ria, Naked Portrait 2006-7. Ria's head is a coarse impastoed lump, the bedcover a fastidious off-white rumpled plain, its pattern emerging and disappearing. The painting is marvellous and terrible at the same time, both exhilarating and awful. There's frailty and failure as well as richness and complexity there, which makes it all the better.
Through a sequence of larger and smaller rooms, Freud's portraiture is unpacked, in all its variety, from the thinly-painted acuteness of his 1950s work to his affecting, grand and vulnerable portraits of the performance artist Leigh Bowery, and the mountainous and magnificent Sue Tilley (Big Sue, the Benefits Supervisor). Each has a room devoted to them.
Elsewhere, however, earlier, smaller, works are hung too close together. In some rooms there are too many confrontations and painted intimacies to take in. It's going to be tough when the crowds arrive.
Neither a realist nor an expressionist – though there is as much reality as there is expression in his art – Freud depicted the psychological tensions between himself and his subjects. His paintings are full of life. There is always a palpable atmosphere, even if it is often conjured from dead time in the studio, his models' lassitude or alertness, a sense of someone waiting for those interminable sittings at their appointed hours to be over.
Freud almost always found something new, or a new way to describe, the experience of being in a room with someone else. It was usually the same room, with the same bits of furniture and piles of paint-soiled rags.
Details as much as whole paintings arrest me. So many details! The weave of a wicker chair, the paisley pattern on his mother's suit, the halo of light reflected behind a head on a leather seat, the Paddington skyline rippling in the windowpane, iridescent blue nail varnish flickering on a woman's toes.
Freud's paintings always have great and often unexpected moments, things the eye snags on. His was a process of describing sensation and presence, people and things and spaces and light, through the language of painting.
He was continually trying to find new ways to describe the familiar: clasped hands, a man's dangling cock, a cheekbone, a turn of the head. His touch is almost never dutiful or rote.
Freud would steer through a sitter's boredom, their disquiet or their flamboyance or their awkwardness, to find something new in their introspection, their nakedness. His art is wonderfully perverse, and perversity was the method by which it constantly reinvented itself.
Being Sigmund Freud's grandson did not give Lucian any particular insights into his sitters, and he disparaged familial comparisons, but like his grandfather his work was largely concerned with being alone in a room with another, delving into the silence that falls between them, analysing the ongoing situation. This exhibition is unmissable. Go more than once, if you can.
• Lucian Freud Portraits is at the National Portrait Gallery, London, from 9 February to 27 May