Dürer was famous for his drawings.
He drew complex pictures with lines alone. Woodcuts like this Four Horsemen of the Apocalypse made him famous all over Europe before he was even thirty:
Four Horsemen of the Apocalypse by Albrecht Dürer (1498) (public domain photo)
How did he turn everything he saw into lines? How can that work? “There are no lines in nature,” says the Swiss art critic Wölfflin. “Any beginner can learn this if he sits down in front of his house with a pencil and tries to reduce what he sees to a series of lines. Everything opposes this task: the foliage on the trees, the waves in the water, the clouds in the sky. And if it seems that a roof clearly exposed against the sky, or dark tree trunk, must surely be able to be rendered in outline, even in these cases it is soon apparent that the line can only be an abstraction, because it is not lines that one sees, but masses, bright and dark masses that contrast with a background of a different color…”
A painter might say that everything is not lines but masses of color.
But Dürer brought it off with lines, all kinds of lines. “His historical significance as a draftsman lies in his construction of a purely linear style on the foundation of the modern three-dimensional representation of the world.” (Heinrich Wölfflin, in his introduction to his 1923 collection of Dürer’s drawings.)
Dürer wasn’t of course the first to draw with lines. Linear abstraction goes back to prehistoric cave scratches. But he discovered new ways to use those lines. His way of rendering some phenomena has never been surpassed.
One thing that makes his work different from that of other great draftsmen is the double function he gave the lines. They had not only to define form and show movement but also to decorate. They were meant to have an ornamental beauty.
Other great draftsmen use lines to build a picture but their lines aren’t important in themselves: they contribute to the general impression, that’s all. For example, a group of them intended to indicate a shadow will get the artist’s OK even if, taken for themselves, they are an ugly knot. Dürer wants them clean, clear, and pretty.
At least he did once he had found his own way. When he was starting out he used the lines the way everyone else did. Look at the non-ornamental pen scratches he used to show the deep shadow of his hand and the pillow:
Self-Portrait with a Pillow , c. 1491 (public domain photo)
Sometimes when he was older he even went too far. The ornamental pattern of lines seems to stand like a screen in front of the picture. You have to stare for a few seconds at the complex configuration until, a group at a time, the lines turn into those things they are meant to represent:
Christ on the Mount of Olives, 1521 (public domain photo)
Maybe Dürer’s historical significance as a draftsman lies in his line-drawings, as Wölfflin says. But his best-loved drawings, such as this one, are done with mixed media: watercolors and a brush:
View of Arco (1495) Paris, The Louvre (public domain photo)
See this excellent article on Dürer as a businessman.