We were just hanging out in the sun when suddenly a bunch of guys in black shirts started marching down one of the streets on the square, with a police escort but not too big. Somebody told me it had to do with football, but really, it looked more like some nationalist kind of thing. I'll post a picture of that later, and perhaps a Pole on Pbase can tell me what it was all about. Right after that, this gay rights/gay pride parade started; the police presence was so heavy (in addition to the men on foot there were water cannon, police vans and countless squad cars) you could barely see the marchers.
There is always something happening on Market Square, which is the largest city square in Europe. It's filled with tourists, but it also seems to be a real center of the city for residents as well.