Westminster Hall, built in the 11the century, is the oldest part of the complex. A precursor to cathedral design and one of the first examples of architects figuring out how to build big, it was the largest enclosed building in Europe at the time. In its early days, the hall had semi-permanent rooms and shops (which would be removed when a big trial or something had to take place).
There's stained glass at the end of the hall, but it's washed out in this picture.