How many Witcher schools are there and where are they located?

I've been trying to find the answer to this, but I haven't succeeded.

I think the only information in the books about this is three schools being mentioned by Vezimir and a head-hunter in possession of a gryphon, cat and wolf medallion.
Since The Witcher 2 introduces the Serpent school, I guess there's more, while only those three are known throughout the Northern Kingdoms.

Oh and the three combat styles of TW1 being symbolized by gryphon, cat and wolf suggest that 'school' does not mean 'academy' but 'way of teaching' (somewhat like in asian martial arts). But then again, it is possible that each academy teaches in one way, suggesting that there's 4 (or more) academies.

As far as I know, Kaer Morhen is the only academy mentioned in the books. So, it is unknown if, but likely that there are more. Coen for example is mentioned to come to Kaer Morhen for the first time in one of the books. Since he's already a Witcher, there has to be another academy.

It's nothing Sapkowski gave quite a lot of details about, so it's a lot of guessing and fitting hints together.

As Aaden said, the books provide concrete names only in regard to three schools:
The School of Wolf, of Cat, and of Gryphon.
The game adds the School of Serpent.

Also, Coën (in the books) is from the far north, but his school is never specified.

I bet there were more but, by the time the novels started, wichers were a "dying" species and their own knowledge was dwindling. The prophecy of the great winter itself is actually a prophecy of a coming of increasingly homogenous human world, without magic, elves, dwarves, and monsters. I guess that is why Sapkowski didn't detail these schools, it was supposed to give an impression of change.

Thanks, that explains why I haven't been able to find anything.

I was under the impression the fighting styles were borrowed from other cultures, not specifically formed from the witcher schools, but adapted for use by them.

What I was originally trying to figure out was if there were other locations besides Kaer Moren where there might have been a library that would preserve the processes and recipes for the Trials and mutations, but I guess if the world is turning away from magic, there won't be a need for more witchers (such a sad thing).

I had also wondered if the abbey where Geralt recovered so often (well, so often according the the only two books in English, which isn't really representative) might also hold those secrets.