The Beginnings of Sleep 

During the earliest phases of sleep, you are still relatively awake and alert. The brain produces what are known as beta waves, which are small and fast.
As the brain begins to relax and slow down, slower waves known as alpha waves are produced. During this time when you are not quite asleep, you may experience strange and extremely vivid sensations known as hypnagogic hallucinations. Common examples of this phenomenon include feeling like you are falling or hearing someone call your name. 

Another very common event during this period is known as a myoclonic jerk. If you have ever startled suddenly for seemingly no reason at all, then you have experienced this phenomenon. While it might seem unusual, these myoclonic jerks are actually quite common. 

NREM Stage 1 

Stage 1 is the beginning of the sleep cycle and is a relatively light stage of sleep. Stage 1 can be considered a transition period between wakefulness and sleep. 
In Stage 1, the brain produces high amplitude theta waves, which are very slow brain waves. This period of sleep lasts only a brief time (around five to 10 minutes). If you awaken someone during this stage, they might report that they were not really asleep. 

NREM Stage 2 

During stage 2 sleep: 

• People become less aware of their surroundings
• Body temperature drops
• Breathing and heart rate become more regular

Stage 2 is the second stage of sleep and lasts for approximately 20 minutes. The brain begins to produce bursts of rapid, rhythmic brain wave activity known as sleep spindles. Body temperature starts to decrease and heart rate begins to slow. According to the American Sleep Foundation, people spend approximately 50% of their total sleep in this stage. 

NREM Stage 3 

During stage 3 sleep: 

• Muscles relax
• Blood pressure and breathing rate drop
• Deepest sleep occurs

This stage was previously divided into stages 3 and 4. Deep, slow brain waves known as delta waves begin to emerge during stage 3 sleep. This stage is also sometimes referred to as delta sleep. 
During this stage, people become less responsive and noises and activity in the environment may fail to generate a response. It also acts as a transitional period between light sleep and a very deep sleep. 
Older studies suggested that bed-wetting was most likely to occur during this deep stage of sleep, but some more recent evidence suggests that such bed-wetting can also occur at other stages. Sleepwalking also tends to occur most often during the deep sleep of this stage.

REM Sleep 

During REM sleep: 

• The brain becomes more active
• Body becomes relaxed and immobilized
• Dreams occur
• Eyes move rapidly

Most dreaming occurs during the fourth stage of sleep, known as rapid eye movement (REM) sleep. REM sleep is characterized by eye movement, increased respiration rate, and increased brain activity. The American Sleep Foundation suggests that people spend approximately 20% of their total sleep in this stage.
REM sleep is also referred to as paradoxical sleep because while the brain and other body systems become more active, muscles become more relaxed. Dreaming occurs due to increased brain activity, but voluntary muscles become immobilized. 

The Sequence of Sleep Stages 

It is important to realize that sleep does not progress through these stages in sequence. Sleep begins in stage 1 and progresses into stages 2, and 3. After stage 3 sleep, stage 2 sleep is repeated before entering REM sleep. Once REM sleep is over, the body usually returns to stage 2 sleep. Sleep cycles through these stages approximately four or five times throughout the night.
While sleep is often thought of as a passive process, research has shown that the brain is actually quite active during different stages of sleep. Sleep plays an important role in a number of processes, including memory consolidation and brain cleanup.

Source:
https://www.verywellhealth.com/the-four-stages-of-sleep-2795920