Can I use other filters over the UV filter on my DSLR?

I just bought a Nikon D3100 camera and I also purchased a set of 3 filters. I attached the UV filter more as a way to protect the lens itself than anything. My question is, can I use the other 2 filters over the UV filter (they just screw on) or do I have to remove the UV filter in order to use one of the others?

Added (1). Thank you for the response, NickP. I'm so new to this… In which situations would I use each of the 3 filters? I have UV, polarizing and a fluorescent light correction (I guess that one would be used under fluorescent lights, huh?

Added (2). Thank you "Al the Pro"! Very helpful! I'm learning little by little. )

The more glass objects you add to the lens the more the image degrades. If you never go beyond 4x6 or 5x7 prints, you will never see anything. BUt an 11x14 or 16x20 may be another situation. I have always taken the filter off the lens and replaced it with the one that I want to influence my outcome.

If you screw on too many filters, you can get vignetting at the corners, especially on wide angle lenses.

The UV filter is of little use other than protecting the lens from damage. UV filters don't do much to correct haze for digital cameras.

The fluorescent correction filter would not likely be used much as your camera should automatically adjust it's color balance when shooting under fluorescent lighting.

The polarizer (if it is a circular polarizer) on the other hand can be useful in removing reflections from light onto glass, intensifying the sky, and cutting down on reflections on the water.

Make sure though the the polarizer is a circular polarizer and not a linear polarizer. In film, linear polarizers were used, but they interact with digital cameras exposure and autofocus systems.

Al and Nick are right.

One question: Why would you use a FL filter?

Your camera has an excellent white balance that is more accurate than any FL filter, FLD or FLB Look on page 88 of your user manual to see how extensive that correction can be.

Yes you can. UV is more for protection. Keep it on at all times except when doing very long exposures like 30 seconds or above to avoid glare from building up inside the lens.

Polarizers cut light in the same way as blinds on a window does. The slits are good for limiting light from one angle only making it useful for eliminating reflections from eyeglasses, glass windows, the swimming pool and other water sources.

Fluorescent light comes out unnaturally green on camera. The filter corrects it to normal hues. You can use it when you are shooting under fluorescent light and the white balance in the camera can't get it right whether you set it to auto or fluorescent. Set your camera to daylight when using the fluorescent filter under fluorescent light.