8x8 LED Matrix on Arduino Nano

SecondSun:
I fiddled around a little bit, but got more and more confused. I must be doing something fundamentally wrong. Any ideas?

There are two basic types of 8x8 LED matrices.

row anode column cathode
row cathode column anode

which one do you have?

You also don't have any current limiting resistors for your LEDs. Not good.

https://www.arduino.cc/en/Tutorial/RowColumnScanning
.