The Institute

The Institute is likely the descendant of the Massachusetts Institute of Technology, located within the Commonwealth. Little is known about Institute other than that the scientists working in the sealed environment of the institute possess highly advanced technology and technological skills. The Institute has created true AI and is capable of creating convincing androids.

In fact, it seems that aside from the Enclave, the Shi of the West Coast and a few scattered groups of individuals, it is the only organization in the post-Apocalyptic wasteland that continues to pursue scientific study and technological development.

Another organization active in the Commonwealth, the Railroad, functions in direct opposition to the Institute, as their goal is to free sentient androids from their creators.

Contrary to fierce arguments from The Railroad, there is not much evidence provided to demonstrate that they are either "good" or "evil"; in The Replicated Man, Dr. Zimmer simply wants to safely recover his creation, and when aided in this, he lectures the android on the advantages of staying in the Commonwealth, and leads him unharmed (or simply reset) out of Rivet City.

Broken Steel
In Fallout 3 ' s Broken Steel DLC it is mentioned that Dr. Madison Li supposedly went north to join the Institute after the events of Take it Back!. Whether this was truly her intention and whether she actually made it there is unknown.

Trivia

 * The Institute itself could be a reference to Logan's Run. The place is noted as being a technologically advanced, sealed environment, and Harkness mentions a history of killing "Runners" with a plasma rifle before escaping himself.

Appearances
The Institute is only referenced in Fallout 3.