Vrubel had a law degree, but then studied painting at the Imperial Academy of Art in St. Petersburg. For a few years he worked on a project in Kiev to replace 12th century murals and was able to travel to Venice, but also began to work on images of a demon based on an epic poem by Mikhail Lermontov. His first Demon painting in 1890 was noteworthy enough to launch his career. This and more biographical in formation can be found here and here.
Vrubel could vary his style, but his best-known paintings feature a good deal of square-brush work to create a fragmented, jewel-like effect around more smoothly painted faces and other features of his subjects. The best place I know of to view Vrubel's art is in Moscow's State Tretyakov Gallery a short distance south of the river bordering the Kremlin. When I was there, an entire room was devoted to Vrubel.
Pencil and gouache. I include this to show Vrubel's approach early in his career. Later drawings were more wispy with plenty of possibly excess lines included.
The artist's opera singer wife. This was painted not long before he lost his sight. Vrubel was not completely wedded to the square-brush - jeweled effects he is most famous for.
As noted, he made several Demon-themed paintings, and this is the first and most famous.
His wife depicted in a role she sang in a Rimsky-Korsakov opera. Another of his best-known paintings.
Vrubel continued the Demon a dozen years after the first painting.
More of a sketch than a finished work here.
Absent the woman, this would be an abstract painting.
Another classic Vrubel image.