The Foundation universe refers to the universe of the Foundation series, in which are set many books and short stories either written by Isaac Asimov or authorized by the Asimov estate. It spans the Milky Way galaxy and ten thousands of years in the future, with events diverging from the real history in the second half 20th century, the first obvious event being the Great Catastrophe in the 1970s.
The works belonging to it include the Foundation series, the Galactic Empire trilogy (and one Galactic Empire short story, "Blind Alley"), and the Robot novel series and Robot short stories, as well as some books written by other authors authorized by Asimov's estate: the Isaac Asimov's Robots in Time, Robot City, Robots and Aliens (all three arguably, with inconsistencies) and Robot Mystery series by various authors, the Caliban trilogy by Roger MacBride Allen, the second Foundation trilogy by Gregory Benford, Greg Bear and David Brin, and the I, Robot prequel trilogy by Mickey Zucker Reichert. They are all sometimes called "the greater Foundation series" together.
There are also some books and short stories which are implied to be part of the Foundation universe, but are not definitely part of it. These include Nemesis, The End of Eternity and the short story "The Last Question".