Short answers, pulled from the story.
Abstract art uses the visual language of shape, form, color, and line to create a composition that may exist with a degree of independence from visual references in the world. It departs from accurate representation, and that departure can be slight, partial, or complete. Total abstraction bears no trace of any reference to anything recognizable.
Early intimations appeared in the late 19th century, including James McNeill Whistler's 1872 painting Nocturne in Black and Gold: The Falling Rocket and Georgiana Houghton's spirit drawings exhibited in 1871. Many experimental works pursuing pure art were created between 1909 and 1913, and Kasimir Malevich completed his first entirely abstract work, Black Square, in 1915.
Pioneers of abstraction included Wassily Kandinsky, Frantisek Kupka, Robert Delaunay, Piet Mondrian, Kasimir Malevich, and Hilma af Klint. Kandinsky painted his Untitled First Abstract Watercolor in 1913, and Mondrian developed his Neo-Plasticism of horizontal and vertical lines between 1915 and 1919.
Fauvism, developed by Henri Matisse and artists including Georges Braque, Andre Derain, Raoul Dufy, and Jean Metzinger, used color conspicuously altered against reality and directly influenced Kandinsky. Cubism, based on Cezanne's idea that nature can be reduced to cube, sphere, and cone, altered the forms of real entities. Together they opened the door to abstraction in the early 20th century.
Mysticism and modernist religious philosophy shaped abstract art deeply. The theosophist Mme. Blavatsky influenced Hilma af Klint and Wassily Kandinsky, while Georges Gurdjieff and P.D. Ouspensky influenced Piet Mondrian. The Theosophical Society popularized the sacred books of India and China, and artists sought an objectless state and an inner object through geometric shapes like the circle, square, and triangle.
During the Nazi rise to power in the 1930s many artists fled Europe, and by the early 1940s exiled Europeans including Marcel Duchamp, Fernand Leger, Piet Mondrian, Max Ernst, and Andre Breton had arrived in New York. The climate of freedom there gave rise to the Abstract expressionists and the New York School, with figures such as Mark Rothko, Jackson Pollock, Robert Motherwell, and Franz Kline.