Greetings all! I am completely new to Arduino (just finished my first version of the "Blink" program

) and I want to know if Arduino can do the following. If it *can* I'd like to know so that after I finish my first tutorial guidebook I'll know what kind of tutorials or knowledge to seek out!
Okay, so what I'm working on is a coffee table with LEDs in it. Basically it will be a 2'x4' rectangle with about 75 LEDs placed in the table underneath a glass sheet. What I'd like to be able to do though is write some sketches that control what lights are lit at certain times. So I'd like to be able to turn on all 75 lights, or cycle through the lights one at a time, or have the lights "chase", or light half of them, or blink a just the ones on the outer perimeter of the table, etc...
I think I'm asking if the Arduino can control many more lights than it has outputs? I think pinball machines do this my using what's called a "light matrix" where they have up to 64 lights controlled by only 16 wires in an 8x8 setup. Does the Arduino allow for anything like this?
If so, what is this called so I know what to start studying!