When Antoni Gaudí died in 1926, at the age of 73, tens of thousands attended his funeral: it was as if a saint had died. His legacy consisted not of money, but of some astounding buildings, not least his unfinished cathedral. After his death, other European architects first ignored and then forgot him, thinking that he had nothing to teach him.

Example of Gaudí's architecture include the Casa Batlló, built in 1905 to represent the legend of St George and the Dragon: the roof was the dragon, the cross St George, the chimneys the dragon's claws, while the elaborate shapes adorning the façade represent the bones of its victims.

When Gaudí took on a project, he insisted on executing everything himself, right down to the furnishings. As a young man, he was a brilliant mathematician, but there were also signs of the extreme religious insight and personal simplicity which would mark his maturity.

He designed everything in the Colegio de las Teresianas, built in 1889, including the gates, a craft he may have learned from his coppersmith father. Its distinctive arches were based on a mysterious equation that he had developed to produce a shape between a parabolic arch and the embodiment of the three persons of the Trinity.

Gaudí's native province was the remote and isolated Catalonia. As a young man he worked as an associate architect in the monastery of Montserrat, 40 miles from Barcelona. He was fascinated by the local rock formations, which looked as though the stone was dripping, and this became a recurring element in his own architecture. He was influenced by Art Nouveau, but his own work was strange and uncomfortable, far removed from the normally prim respectability of the idiom.

The tree-like columns of the Santa Colona chapel are less eccentric than they look, because they represent new ideas of what columns can do: they are holding up the ceilings without buttresses, which Gaudí hated. All these projects - which included viaducts, ceremonial arches and schools - were ultimately experiments for his cathedral.

He was an engineer of genius, constructing a notion of architecture that banished the straight line, as this did not occur in nature, and at the highest point of everything he installed a cross. The Park Güell, built in 1900, was originally a housing estate but is now a Barcelona park. Its use of collage foreshadowed the Cubists and Surrealists of several decades later. The Casa Milà of 1905 was even more radical, its roof inspired by the action of the waves along the seashore. Its distinctively shaped ventilators and chimneys were originally designed to surround a huge figure of the Virgin Mary, which was never completed.

Gaudí's unfinished Cathedral of the Holy Family was his masterpiece, incorporating everything he stood for: brilliant engineering, oddness, abstractions, structures with no architectural precedents, "dripping stone", Art Nouveau, naïve and almost medieval storytelling, and the ability to think on a vast scale. Seventeen towers were planned, the central Christ tower intended to be twice as high as the four that were completed.

He hardly ever made drawings, and kept no notes, and although he constructed models, many of them were smashed and burned when his workshop was trashed during the Spanish Civil War. Surviving fragments have since been analysed to discern his intentions for the cathedral, and it is intended that construction will continue. Gaudí himself is buried in what would have been its nave.