Visual art review: Becoming Picasso: Paris 1901 - Portrait of the artist as quixotic genius and grieving friend

In one year, Picasso staged his first show, lost his soulmate, and forged the giddying range of styles that revealed his pedigree and future

The Courtauld Gallery's new show has a catchy title that prompts a question: becoming which Picasso? There were, after all, several – Picasso the Surrealist, the Classicist, the Analytic and Synthetic Cubist; the Blue Period Picasso, the Rose Period Picasso .... Which will we find as we climb the steep stairs in Somerset House?

And the answer is, none and all of them. Becoming Picasso deals with a single year in its subject's life, 1901 – the moment when he launched himself with an exhibition at the gallery of Ambroise Vollard, champion of Cézanne, protector of Gauguin, promoter of Vincent van Gogh. Picasso was 19 when the show opened in June. He was other things as well: classically trained, Spanish, 19th century. Above all, becoming Picasso meant coming to Paris – being a Parisian painter but also not, stealing just enough from Degas and Manet to build a French Trojan horse for his own Spanish genius.

That spring, he worked like a mad thing. Picasso showed more than 60 works at Vollard, all of them new, all made in a studio in Montmartre. How many canvases he painted and did not show, we can only guess: certainly, he could turn out three a day, and did. Most of the 18 pictures at the Courtauld were at Vollard, but not all. As well as the famous five dozen, he painted scores more in 1901, in so many styles and genres that even the small sample here makes your head spin. Becoming Picasso is the picture of an artist on fire.

Almost literally so in the case of the self-portrait known as Yo – Picasso, ("I, Picasso"). The nickname comes from the inscription in paint to the left of Picasso's face, although, in a sense, it is a tautology. A less aggressive but equally insistent message is his signature – the simple "Picasso" that would adorn all his work for the next 70 years, replacing the patronymic "Ruiz" he had used in Spain. Yo – Picasso is a 19th-century swagger portrait, Spanish – its immanent light is like that of Goya's Condesa de Chinchon – but radically new too: painters did not daub slogans on their canvases in 1901. A self-portrait, it also depicts that spring. Between Picasso's cravat and the edge of the canvas is an area of orange paint, jabbed on with an open brush, alive with energy. It is like staring into a flame.

As a statement of intent, though, Yo – Picasso arguably ranks second to La Nana (Dwarf-dancer). In the 1840s, French artists, in the Louvre's new Galerie Espagnole, had discovered Spanish painting. ("Discovered" is not putting it too strongly: in 1688, the historian André Félibien had described Velázquez as "an unknown".) To Picasso's annoyance, the genius of Spain was now viewed as an inheritance of France. La Nana is a response to this, flicking two Hispanic fingers at the French claim. Picasso's dwarf is rude, black-haired, glowering with Spanish attitude – Degas' Little Dancer Aged Fourteen morphed with the dwarf Maribarbola from Las Meninas. With her bunched left fist, she looks as though she is ready to take on all comers – as was the man who had painted her.

In this are glimpses not just of the later Picassos but of Postmodernism. Yes, the Spaniard plays Parisians at their own game – Gauguin and Manet in Absinthe Drinker, Toulouse Lautrec in At the Moulin Rouge – but there is irony in the brazenness of his stealing. La Nana's ballet-shod feet, in fourth position, both echo Degas and mock him. In the same way, the black outlines of his harlequin pictures are unabashedly from Gauguin, but they tell a story that has nothing to do with Cloisonnism or Pont-Aven.

In February 1901, Picasso's friend and countryman, the painter Carlos Casagemas, unlucky in love, had shot himself in the head in a Paris café. Spelled out in the melancholy of Seated Harlequin is a sorrow so deep that it can only be told in mime: the two fingers the pierrot points at his temple echo Casagemas's mode of suicide. Beyond this is Casagemas in his Coffin, the first picture in the show that is less about where Picasso was coming from than where he was going: in its deathly hues are the roots of the Blue Period.

A second self-portrait was painted weeks after the first. The gulf between the two is vast. Self-Portrait (Yo) is less Goya than Munch, a soul-painting – a response, perhaps, to the Norwegian's lithographic Self-Portrait with Skeleton Arm of 1895. "I live with the dead," Munch had said; now Picasso did, too. In fewer than 20 works, the Courtauld tells a story that leaves you aching for the next instalment, to know those other, later Picassos. It is a customarily brilliant show.

To 26 May (020-7300 0500)

Critic's Choice

Get in line! The Royal Academy's Manet show is a predictable hit; with a focus on portraits, it offers a wide survey of the artist's impressive output. Booking is necessary, but you have until 14 Apr to catch it. Another worth-the-queue exhibition is the Hayward Gallery's Light Show, featuring works by 22 artists (with a stand-out installation by James Turrell). It's illuminated until 28 Apr.