Isaac Asimov wrote the Foundation universe books throughout his life. He had at first intended to write "Foundation" only, but the whole thing probably expanded beyond his control. After reading most of the books and stories listed here, I have come to believe that he did not intentionally write them as part of one universe. They just turned out that way.
The Foundation Universe has 3 books at the core: Foundation, Foundation and Empire, and Second Foundation. These books are preceded and followed by several others, and the narrative order is: (roughly)
The Robot Series
(involving USRMM and Dr. Susan Calvin)
The Positronic Man
(with Robert Silverberg)
The Caves of Steel
(The 1st book featuring Daneel Olivaw)
The Robots of Dawn
Robots and Empire
The Stars, Like Dust
(not directly related, but can be fitted in)
Pebble in the sky
Prelude to Foundation
Foundation
Foundation and Empire
Second Foundation
Foundation and Earth
Please try to read these books in the same order, except
'Forward the Foundation', which MUST be read last.
WARNING:
Do not zoom to the end of 'Foundation and Earth' directly,
there is a major revelation there...