This is a shattering show beautifully represented. It is an incomparable record of the last throes of the 20th century. Henri Cartier-Bresson (1908-2004) is the father of modern photography. He was French, astute, civilised, he was trained as a painter and versed in art history. Early on in life he had studied the photos of Eugne Atget, his sober turn-of-the-century records of Paris shops and trades. With his trusty Leica slung around his neck at all times, Cartier-Bresson travelled far and wide, allowing the new and unfamiliar to spur the freshness of his vision. His curiosity and his insatiable eye were boundless. Not only did he observe all walks of life, the humble and the odd moments, but he was an intimate of all the best and most brilliant artists and writers of his time all over the world. Towards the end of his life he gave up photography and devoted himself to drawing. But since this is not about immediate discovery, he was not outstanding in it, though for once satisfied with process. His lens could be relentless, revealing, gentle, chilling, soothing, but it was always astonished.

The blinking man watching a bull-fight in Spain; those stark men dressed as women outside a brothel in Mexico; the little boy jumping before a black-spattered wall; the French collaborator shamed in public; Madame Curie sharp and kind; Jean-Paul Sartre one-eyed by the Seine and a host of other ever-vivid and perplexing scenes are now embedded in the collective memory, part of our cultural treasure.

But before we become overwhelmed by the wealth of its material, the surprise of the show at Museo di Roma is that it wisely begins with a homage to Rome. It consists of pictures done in different periods from different visits, most of them done right after world war two, when the city was poor and sober and bare of tourists and full of simple Romans. A little girl sainted by a square of sunshine in a cobbled piazza; Zro de Conduite little knobby-kneed boys playing soccer in bleak empty lots in the borgate; scant fruit sparingly and prettily arranged on a crate; tear-stained faces of nuns moved by the election of pope Roncalli, Giovanni XXIII, in 1958.

This little-known Roman section is followed by display cases full of letters and publications, instructive and evocative material not just for the student. But of course a portrait gallery of the brilliant people of our times, their faces flickering with thought, with lively attention, sadness or humour, seems inexhaustible. They pose with candid ease for Cartier-Bresson, their friend, shy or bold: Matisse fondling his doves, Bonnard, Giacometti, Miro, Bacon, Chagall, Duchamp, Sandy Calder, Saul Steinberg wickedly smiling with his cat, Jung, Oppenheimer the physicist, Neru, Beckett, Martin Luther King, Piaf, Coco Chanel, Colette, Barbara Hepworth, Leonor Fini, Simone de Beauvoir, Arthur Miller, Breton, Dior. And lots of others without whose presence our world would have been sorely diminished.

In contrast to the above contributions, all positive, Cartier-Bresson also throws a negative revealing light on our little planet, shown in a film called Flagrant delits or Flagrant Crimes in a series of absolutely pitiless scenes. The film has the bad manners of a bad documentary but poignant music by Diego Masson. It crops and cuts pictures arbitrarily so distorting their impact, it zooms in and out trying to jazz up still shots to make them look like a movie.

But in it are Cartier-Bresson mass scenes. They are devastating: thousands are trying to climb trains, thousands of dervishes writhe on the ground in India; thousands march in China; thousands wait in line at Lenins grave and indulge in hearty gymnastics in Russia; they crowd at the races and soccer in England these are a series of ferocious accounts of our world where people swarm and act like ants.

Photography is a medium that demands no manual craft, skill or patience. It is entirely dependent on the flash of intuition, on the instant, on intelligence of vision. It is something abruptly and mechanically distilled on flat paper, not painstakingly built up. Very few have had the ability to master photography and make an art of it, but Cartier-Bresson with his diamantine black and white stills stands out like a beacon over todays avalanche of photography.

You lay your own head, your own eye, your heart on the line, he said. His marvellously sharp eye saw, he snapped, he caught the live moment and stilled it like a bee in amber, gathering a mosaic of humdrum things into one lyrical inexplicable whole.

Henri Cartier-Bresson. Homage to Rome.

Portraits. Publications. Flagrant Crimes, film. Until 29 October.

Museo di Roma, Palazzo Braschi, Piazza S. Pantaleo 10, tel. 0682059127.