Can anyone tell me what is difference between nachdem, danach, nach,
i always confuse with german words, Nachdem, Danach, Nach.

Question

Answer

All of these 3 words have a similar meaning, describing that something happens after something else. The difference between them is the grammatical context:

"Nach" is a preposition. It is used together with a noun which describes the previous event. Some examples: 
- Nach dem Frühstück gehe ich in die Schule.
- Nach der Schule gehe ich wieder nach Hause.
- Er fing nach dem Ende seines Studiums eine Arbeit in einer anderen Stadt an.

"Nachdem" is a conjunction that introduces a subclause. So it requires a verb, together with a subject and possibly an object and further elements of a sentence. Some examples: 
- Nachdem ich aufgewacht war, bereitete ich mein Frühstück vor.
- Nachdem ich von der Arbeit nach Hause gekommen war, ging ich mit dem Hund spazieren.
- Nachdem er sein Studium mit einer guten Note abgeschlossen hatte, zog er in eine andere Stadt, um dort zu arbeiten.

"Danach" is similar to other words starting with "da": This "da" is translates to "that", hence "danach" means "after that". It always refers to an event which has been described in a previous sentence. For example: 
- Er frühstückte zu Hause. Danach ging er in die Schule.
- Seine Arbeit endet um 17:30 Uhr. Zehn Minuten danach fährt sein Bus.
- In Heidelberg studierte er Medizin. Danach fand er eine Arbeitsstelle in einem Krankenhaus in Hamburg.

As you can see in the examples, you can express very similar things with the three words. The main difference is the type of grammatical structure you choose.

Answer

Nachdem: this conjunction expresses anteriority: Nachdem ich gegessen hatte, legte ich mich hin. After I had food, I took a nap.
Nach: as a preposition it expresses a certain aim: Ich fahre nach Indien. I go to India. Used as well temporal: Nach dem Abendessen. After dinner. ('nach' can be used as an adverb as well, but this is probably not what you are looking for)
Danach: temporal: Eine halbe Stunde danach kam er wieder. He came again after half an hour. 
Other usage: Die Eltern gingen voran, danach kamen die Kinder. The parents went ahead, the children followed (came after them).

Answer

There are different usages and I gave you here some basics. Hope it well help you for a start.

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