Topkapi was the palace of the Ottoman Sultans. First constructed after the Islamic takeover in 1552, many additions have occurred since then. The various ruling Sultans lived in this palace until the 1800's when they started building more modern palaces along the shore of the Bosphorus.
There are many individual rooms. In some you can take pictures, but not in all. Most of these pictures are either from the library or the room of holies, which contains many religious relics. The treasury rooms (4 of them) contain the jeweled treasure: crowns, thrones, the famous Topkapi Dagger, encrusted with diamonds, saphires, etc. The 5th largest diamond in the world is in this room. But no pictures allowed.
In Topkapi, it isn't so much the architecture or the building, but the workmanship and artifacts, that are impressive.
The entrance at the Imperial Gate
The inner, or third, courtyard
The library, the Sultan's reading room
Various examples of tile work
Continue to Blue Mosque, Mosaic Museum and Basilca Cistern