You should read greek mythology - what sentence is this

I am not sure what kind of sentence types you are comparing it to, but that sentence is an imperative sentence and an independent clause. It is also in the second person point of view. 

Imperative sentences are one of the main four types of sentences (the others being exclamatory, interrogative, and declarative). An imperative sentence can be identified when somebody is telling someone else to do something, or is trying to express a desire or wish. In your sentence, the narrator is suggesting that you read Greek mythology, meaning that in a way, they are expressing their desire for you to do that. 

Independent clauses are just sentences that are not fragmented and share a complete thought. "You should read Greek mythology" is a complete thought and is classified as a normal sentence.

This sentence is also in the second person point of view since it lacks quotation marks. The second person POV is identified as when the pronouns being used are limited to only 'you' and 'your.'

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