Yes ;)

REM sleep is amazing sleep!

REM rebound involves the tendency for REM sleep to increase following REM sleep deprivation.

REM (Rapid Eye Movement) sleep is active sleep.

3/13/2012 jhh: REM sleep is NOT deep sleep. In fact, it is the lightest stage of sleep. In order from awake to deep sleep: AWAKE, REM, LIGHT, DEEP. Deep sleep and REM sleep are the most important stages though. Light sleep doesn't do much for you. Deep replenishes your body, while REM replenishes your mind.

Older answer (not accurate):

Yes. It is the deeper form of sleep that we experience during our sleep cycle, rem sleep is where dreaming occurs

But not the deepest sleep, which would be delta. That's where, unless your a mother and hear your baby cry, you are oblivious to your environment.