I saw here Table of broadcasting stations that there is a mode called DMR (under Atlanta Technical College). What is DMR and if I buy a scanner (I am thinking about the Icom IC-R6) could I listen to those stations?
DMR stands for Digital Mobile Radio. It is a digital voice and data protocol that can be used unlicenced or commercially. You can peruse a standards document if you like.
One of the major issues preventing you from using just any scanner from tuning to DMR is that the vocoder being used is AMBE, which is proprietary. Your scanner, in addition to needing support for digital voice, must have an AMBE codec chip in order for you to be able to decode (and, by extension, listen to) the audio data. (The ICOM IC-R6, sadly, supports neither. You will have to find a different product, such as a DMR handheld, if you are interested in receiving this mode.)
You might be able to listen to DMR using scanner, if the scanner itself is appropriate, that is to say how simple it is to get to the output signal produced by the scanner's discriminator.
The catch is that you'll need to use a computer to decode the DMR signal and to give you useable output. There is software, like for example Digital Speech Decoder which are capable of providing you with decoded DMR. DSD is commonly used for scanning together with RTL-SDR dongles and it works fine for decoding DSD in that use.
I myself have no experience with IC-R6, so I cannot provide good recommendation about its suitability, but the specifications I managed to find on the Internet make me skeptical of its out-of-the-box suitability due to mentions of "low-pass filter". Baseband width of DMR signal is a bit wide and I fear that it could be wider than the passband of the IC-R6's low-pass filter.
From what I can see, it is possible to obtain the unfiltered output from the IC-R6's discriminator itself, but I don't know how complex the modification would be.