• Dormir is a static state: (to sleep, to be sleeping).
• (S’)endormir is the transition between being awake and sleeping (to fall asleep/to put to sleep)
• (Se) rendormir is is the same as endormir but when happening after waking-up (to fall asleep again/to put to sleep again)

The last two verbs are usually pronominals.

Dormir describes the action of going to sleep on purpose.
Like “Je vais aller dormir” for “I am going to sleep”

Endormir is more like “falling asleep”, accidentally or against your will.
Like “Je me suis endormi sur mon bureau” for “I felt asleep on my desk”.
Or “Ce prof est en train de m’endormir” for “This teacher is making me falling asleep”.

Rendormir (Usually se rendormir) is used when you were asleep, woke up, and (on purpose or accidantally/against your will) go back to your sleep

Endormi is used to describe the state you’re are asleep.
Like “Elle est endormie” for “She is asleep”

me (m’)/te/se before endormir can indicate it is reflexive verb.

French expresses the various meanings around sleep through prefixation of dormir or uses those derivatives as reflexive verb, whereas in English, to convey the same meanings, we mostly use another verb along sleep or a phrasal verb.

1. Dormir is sleep.

2. Endormir
Prefix en indicates here a change of state¹. Endormir is put to sleep.

Ce genre de musique m’endort¹.

This type of music puts me to sleep/makes me sleep.    

La maman endort le bébé en lui chantant une berceuse.

 The mother sings the baby to sleep with a lullaby.  

On fait une piqure au malade pour l’endormir.

The patient receives an injection to put him to sleep.

3. S’endormir, reflexive verb, is something we do to ourselves, without outside intervention. Fall asleep / go to sleep

Je m’endors régulièrement à la tombée du jour.

I regularly fall asleep/go to sleep when night falls.

4. Rendormir
Prefix re indicates here the return to a previous state¹. Verb + back to sleep

L’infirmière fit une piqure au malade pour le rendormir.

The nurse gave the patient an injection to put him back to sleep.

5. Se rendormir, reflexive verb.

Je me réveille toujours vers cinq heures du matin mais je me rendors toujours.

I always wake up around five but I always go back to sleep.

<sub>1. It has several other meanings.
2. m’ is the object personal pronoun, it does not indicate here a reflexive verb.
3. re+endormir → rendormir: one e.</sub>