SELWYN COLLEGE, Cambridge, is still the only Oxbridge college that has a motto in Greek rather than Latin: ΣΤΗΚΕΤΕ ΕΝ ΤΗ ΠΙΣΤΕΙ ΑΝ∆ΡΙΖΕΣΘΕ. "Stand firm in the faith; act like a man."

Since the 1970s, when the college was among the first in Cambridge to admit women, as dons and students, the more acceptable paraphrase has been "Stand firm in the faith and be the person you are called to be."

Gender differentiation passed St Paul by in writing 1 Corinthians 16.13, but the sense of "becoming" is a richly laden caravel for theologians and philosophers alike. Who are we, and when do we become the person we are called to be? In our teenage years, growing into adulthood, we come closest to exploring this potentiality consciously.

The current exhibition at the Courtauld Gallery delves brilliantly into this, observing Picasso at the age of 19. It is reckoned that Picasso may have produced more than 120 paintings in 1901 alone. Here, just 18 momentous works chart the challenges faced by an artist on the cusp of coming of age.

Confident, full of life, invincible, and determined to establish himself, Picasso gazes back at us from his self-portrait, Yo Picasso: "I Picasso." Here I stand and I can do no other. The arrogance and self-assertiveness of the young is encapsulated in a gash of orange for the necktie and the garish downward strokes of his shirt-sleeve.

The face, in a mirror (notice that he holds the palette in his "right" hand), is unflinchingly violent and combative. It is the face of a bull, and will be the central highlight of this summer's exhibition in Barcelona to mark the 40th anniversary of the indefatigable artist's death. In photographs taken at the same time, his eyes are equally penetrating and unwaveringly cold.

The self-portrait (private collection) was listed as the first work in the June 1901 exhibition of his work staged at the Parisian gallery of Ambroise Vollard. It is with that show, for which Picasso produced some 64 paintings, and its aftermath that this quintessential exhibition is concerned.

Picasso had made his first trip from Barcelona to Paris the previous year, in October, shortly before his 19th birthday, with his friend the artist Carles Casagemas, to visit the Exposition Internationale Universelle in the Grand Palais, and to see how Bohemian life in both cities compared.

Picasso had submitted a work to the Spanish pavilion which found favour and brought him to the attention of a small-time art-dealer and agent, the 40-year-old Catalan Pere Mañach. He found sales for Picasso, and promised to arrange an exhibition for him next year.

For three months, Picasso and Casagemas shared a studio and a girlfriend, a young married seamstress and model, Germaine Florentin or Gargallo, as they painted the town red. An increasing alcohol dependency and impotence led the 20-year-old Casagemas on a ruinous path to self-destruction.

After returning home together to Spain in the winter, Casagemas left Picasso there to go back to Paris. On 17 February, he took several friends, including Germaine Gargallo, to supper in his local cafe. Casagemas stood up to make a speech, drew a gun, and fired at her. She dodged the bullet, and he turned the gun on himself.

When Picasso, who was in Madrid, received the news a few days later, he was devastated. He contributed an ink sketch of his friend to the formal obituary in the Catalunya Artistica (28 February), and some time later in the year painted several portraits of his dead friend.

These remained unknown, in the possession of the artist, until the 1960s, when he allowed them to be included in a catalogue of his work, remarking that his friend's suicide had depressed him and contributed to his "Blue Period".

But this did not prevent Picasso's painting or having a fling with Gargallo when he came back to Paris to work towards his exhibition. He shared a flat with the poet Max Jacob, and, through Mañach, met Vollard in June. He was also introduced to some of the fallen women who lived in the Hôpital St Lazare, often with their babies. The women dressed in blue, and wore a white bonnet if they had a sexually transmitted disease. Like the nuns Gauguin often painted, they turn up in his pictures.

Sales from the show were respectable. The suggestion that Portrait of a Man (Bührle Collection, Zurich) is set in the exhibition, and therefore gives a snapshot of the hang, cannot be the case, as we know that Vollard did not frame the pictures; so we still have no reliable depiction of the landmark sale.

Picasso had carried small works with him from Spain, but he painted most of the works shown in Paris at a speed that outraged and amazed commentators, producing as many as three a day. As in his show for the world fair, he included stock Spanish figures in the exhibition: the pouting Dwarf-Dancer ("La Nana"), with her hand on her hip, and an equally grotesque courtesan-like figure of a Spanish Woman seated in a vast crinoline skirt on a settle (Copenhagen), her head defiantly resting on her right hand.

But there is something unreal and unnerving about the way in which the women are observed which forces us to look again when we might want to turn aside. The Spanish Dancer crouching on the floor with her knees drawn up under her chin is more threatening than seductive, even to a 19-year-old Minotaur.

The 1901 show also included the extraordinarily graphic portrait head of a genial hobo, Bibi la Purée (the French have the same aphorism of "being in the soup"), a drinking mate of Verlaine and the toast of Montmartre. His wide forehead and grin suggest Frans Hals as much as Goya. All dressed up and with nowhere to go, this bon vivant flâneur was dead within two years.

The later paintings that Picasso produced include, on one wall for our delectation, Lady Aberconway's Girl with a Dove and three of the great "Harlequin" series of café portraits, with the Seated Harlequin (The Met) lost in thought, gazing across at the Moscow couple, Harlequin and Companion, an enigmatic portrayal of marital ennui which may feature Casagemas and Germaine. Next to them, St Petersburg has sent the abstracted figure of the Absinthe Drinker, painted thinly as if by Gauguin.

The Girl with a Dove hung in the National Gallery from 1974-2010, loaned by the heirs of Lady Aberconway, to whom Samuel Courtauld bequeathed it in 1947. It is probably the first work by Picasso to enter a British collection (it was with the Alexander Reid gallery in 1924), and should be acquired for the Courtauld collection; but this may well be the last chance to see it publicly. This picture should be kept in the UK if we claim to be a nation of culture and distinction.

The last wall is the saddest of all, with an imaginary scene set in the morgue. The gaping wound in Casagemas's right temple has been painted out, as if undertakers have worked their cosmetic posthumous magic. Instead, the artist drowns in the melancholy blue of Picasso's defeatist imagining, swathed in the false comfort of his death clouts. Picasso had read his Nietzsche, and here convulsively painted The Birth of Tragedy.

The vertical narrative of Evocation (The Burial of Casagemas), from the Musée d'Art Moderne, Paris, is a secular and almost blasphemous altarpiece for his friend's burial. Reimagining works by El Greco and Courbet, Picasso, a thieving magpie if ever there was when it comes to artistic inspiration, has staged the apotheosis for his boon companion, attended by the whores of St Lazare and "a Madonna" much like Germaine Gargallo. But the boy done good, and for another 70 years he commanded the art world, as recent auction prices still suggest.

"Becoming Picasso: Paris 1901" is at the Courtauld Gallery, Somerset House, Strand, London WC2, until 26 May. Phone 020 7848 2526 (24 hr recorded information).

www.courtauld.ac.uk