This is the vast, imposing former headquarters of the Stasi (Russian Secret Police). The anti-Stasi graffiti from when the wall came down is still on parts of the building. The building itself is enough to strike fear into people.
Only a small part of this very Soviet building is a museum about how the secret police worked. It is quite cheap to enter and has some fascinating exhibits, such as cameras and other spying equipment, the Stasi used.
There isn't much in English, but if you ask, you can get a booklet explaining every exhibit and item in English. The lovely lady in the tearoom (the unchanged staff canteen was in the Soviet days) even put a video on for us in English.
It was quite scary in many ways, showing the lengths a government went to just to spy on its own people who they were so paranoid of.