I'm a Dummy, Tell Me About Turntable Mats


Turntable mats seem to be an inexpensive way to improve a component, but the thing that gives me pause is that as I understand it, you put them on with adhesive. Is there a possibility that a turntable would be damaged by a turntable mat?

If it's relevant at all, the turntable I'm thinking of using a mat on is a Sota Comet III bought used.
heretobuy
If your goal is to absorb all resonant energy from the LP, then you want a platter surface and/or a mat that most mimics vinyl in its physical characteristics.  For that, Delrin is a good choice.  But other materials work too.  However, if it was as simple as absorbing and dissipating resonant energy in the LP, then everyone by now would have agreed that vinyl-like materials are indisputably the best.  As you can see, this isn't the case.

In my own opinion, you have to try a variety of different mats made of different materials, and then decide for yourself.  I daresay, the same mat might affect the sound of one LP differently from that of another LP.  Worrying about that would be a nightmare.
I have the following mats, Funk Achromat, Soundeck, Herbie's Way Excellent II, and some of the stock mats that came with my tables.  When I had my VPI Classic 2 I didn't use a mat.  Same with a couple of tables that had acrylic platters.  I can't tell major differences between them. 

The only one that I tried that had a significant impact on sound was a deerskin mat that I saw some people raving about.  It made things sound kind of dead.  I don't recommend it.

I wouldn't worry about the adhesive.  The Achromat mat has adhesive, but I doubt I'll ever take it off.  The Herbie's mat is kind of sticky, but no adhesive.
Can I just say that even such illustrious decks as the Air Force One have platter mat options… like cartridges they can be a matter of taste. I am personally trying to get a modern equivalent of the oil filled Sony mat OL 2K for my TTS 8000. I know of many that swear by the copper Micro Seiki - Artisan Fidelity will charge you $995 for a new pure copper equivalent..
Then there’s the Resomat, which suspends the LP in air above a solid surface, supported only on the tips of rubbery points that are fastened to the mat surface. The result is pretty much the exact opposite of the philosophy of absorbing resonant energy from the LP. The LP is left to deal with the resonant energy on its own. Many users swear by that.