Does your dog dream?

I would like to think that my Great Dane does dream! He will be in our bed growling in his sleep like he is in a fight with another dog. Then he will start to kick his legs like he is trying to run away. All while being in a dead sleep. He isn't easily woken up by too much. This dog makes all kinds of noises when he sleeps. I would like to think that he is having great dreams. There would be no other explanation. We have dreams, and i would like to think that he is capable of having dreams as well.