I know the ancient Greek modes and the Gregorian modes of the medieval era. Reading in a comment the term Celtic modes I wonder is there something different or special that I have missed until today?
As we can see in the following link there is no difference between the Celtic modes and the well known medieval modes.
But it seems there are especially 4 modes in use:
Ionian, Dorian, Mixolydian, Aeolian. See:
Complex Tonality and the Four Celtic Modes
Here’s a nice video explaining the mixolydian mode (with the typical b7) in Celtic style: