They are only loosely connected. Their main common points are Asimov's idea of a future Galactic Empire, certain aspects of technology—hyperdrive, blaster pistols, "neuronic whips"—and particular locations, such as the planet Trantor. Another connection was later established with Robots and Empire, where Asimov revealed how Earth became radioactive, as mentioned in The Stars, Like Dust. Some sources further this argument by asserting that The Stars, Like Dust takes place about one thousand years following the events of Robots and Empire.
Interestingly, the short story "Blind Alley" is the only story set in the Foundation universe to feature non-human intelligence (not counting robots and Gaia).
Asimov later integrated them into his all-engulfing Foundation series. Some contortion was required to explain how the robots of the Robot Series are almost completely absent from the Empire novels. In reality, this was due to the magazine editor Asimov worked with at the time (John W. Campbell) disliking robots in science fiction, and discouraging Asimov from including them.
Their main common points are Asimov's idea of a future Galactic Empire, certain aspects of technology—hyperdrive, blaster pistols, "neuronic whips", the possible invention of the "Visi-Sonor"—and particular locations, such as the planet Trantor.
Another connection was later established with Robots and Empire, where Asimov revealed how Earth became radioactive, as mentioned in The Stars, Like Dust and Pebble in the Sky.
Some contortion was required to explain how the robots of the RobotSeries are almost completely absent from the Empirenovels.
The term 'Foundation Series' is often used more generally to include the RobotSeries and EmpireSeries, which are set in the same fictional universe.
The premise of the series is that Hari Seldon has spent his life developing a branch of mathematics known as psychohistory, a concept devised by Asimov and his editor John W. Campbell.
The Foundation Series started as a series of nine short stories, eight of which were published in Astounding Science Fiction magazine (between May 1942 and January 1950) and a ninth, which was written a few years later to serve as an introduction when the series was first published in book form.