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 a handful of groups on the East Coast, it is the only organization in the post-Apocalyptic wasteland that continues to pursue scientific study and technological development, like the Shi or the NCR, though it's probably most similiar to the Boulder Dome.

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 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 add-on 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, which could be a reference to the movie Blade Runner which involves escaped androids.
 * This could also be a reference to the United States Army Medical Research Institute of Infectious Deseases (USAMRIID) in Maryland. This facility was built after President Nixon signed a law prohibiting the USA from making any offensive biological weapons. Its goal now is protecting US soldiers from biological attacks, developing vaccines, and controlling strains of bacteria and viruses. It is said in the book " The Hot Zone " by Richard Preston that the soldiers and officers at USAMRIID commonly refer to it as the Institute .

Appearances
The Institute is only referenced in Fallout 3.