NREM sleep

The phase of sleep in which there is no rapid eye movement.  NREM sleep is typically divided into 4 stages, each characterized by a particular brain wave pattern. 

Stage 1 is very light sleep.  Brain waves transition from alpha to theta waves.   Muscles relax.  The sleeper will be easily awakened.

Stage 2 is a bit deeper sleep.  Brain activity shows alpha and theta waves, with two additional disctint patterns emerging:  k-complexes and sleep spindles.  

Stage 3 begins deep sleep.  Brain activity turns to slow delta waves with some theta waves.

Stage 4 is the deepest sleep.  All delta waves.  

For many years scientists believed that NREM sleep was dreamless, and that REM sleep was identical to dreaming.  Much turns on how "dreaming" is defined and understood by researchers and subjects.  Sleepers awakened from NREM sleep typically report experiences closer to thinking than dreaming, although some do report the vivid and complex sorts of dreams that are usually associated with REM sleep.

Source:

Bulkeley, An Introduction to the Psychology of Dreaming

Dement, The Promise of Sleep