I'm finding it difficult to check these sentences. Could you please help me? Thank you.

1)A ghost appears to Hamlet and asks him to take revenge and kill his murderer, Claudius. At the end of the play Hamlet manages to kill Claudius, but he also dies and his mother as well.
2)Hamlet wants to be sure about what the ghost revealed him. So he arranges a play representing the Murder of Gonzago which is very similar to what had happened to his father.
3)During the play Claudius raises and rushes away showing that the ghost was right. This play is very important because during it the actors become the audience itself (themselves?), that’s why it’s called the play-within-the –play.
4)Hamlet considers death from two different perspectives. At the beginning, he thinks about it as a sleep that makes men free from their sufferings following the medieval perspective which used to consider death as a purification of the soul from the body.
5)Then he imagines an afterlife and he sees it as a sleep with dreams in which your troubles follow you and this is a Renaissance perspective.

1. This is very confusing: Who is "his"? Hamlet? or the ghost? Also the last clause is very awkward. Try again with this one.

http://writing.wisc.edu/Handbook/CommonErrors_PronRef.html
http://grammar.ccc.commnet.edu/grammar/concise.htm

2. ... he arranges a performance of "The Murder of Gonzago," which is ...

3. comma needed; confusing wording; run-on sentence
http://grammar.ccc.commnet.edu/grammar/commas.htm
http://grammar.ccc.commnet.edu/grammar/concise.htm

4. OK

5. commas needed; problem with pronouns
http://grammar.ccc.commnet.edu/grammar/commas.htm
http://grammar.ccc.commnet.edu/grammar/concise.htm

Re-post when you're ready.

Sure, I can help you check these sentences. Here's a breakdown of each sentence and any potential corrections that may be needed:

1) A ghost appears to Hamlet and asks him to take revenge and kill his murderer, Claudius. At the end of the play, Hamlet manages to kill Claudius, but he also dies, and his mother does as well.

This sentence looks fine, but there is a missing comma after "play" in the second part of the sentence. Also, it may be clearer to specify that Hamlet's mother dies as a result of Claudius' actions.

2) Hamlet wants to be sure about what the ghost revealed to him. So he arranges a play representing the Murder of Gonzago, which is very similar to what happened to his father.

This sentence is correct, but "revealed him" should be corrected to "revealed to him" for grammatical accuracy.

3) During the play, Claudius rises and rushes away, showing that the ghost was right. This play is very important because during it, the actors become the audience itself, that's why it's called the play-within-the-play.

This sentence is mostly correct, except for a minor correction in the last part. Instead of saying "the audience itself," it should be "the audience themselves" since "audience" is plural.

4) Hamlet considers death from two different perspectives. At the beginning, he thinks about it as a sleep that makes men free from their sufferings, following the medieval perspective, which used to consider death as a purification of the soul from the body.

This sentence is correct, but a comma is needed after "sufferings" to separate the clauses properly.

5) Then he imagines an afterlife, and he sees it as a sleep with dreams in which your troubles follow you, and this is a Renaissance perspective.

This sentence is correct, except for the use of "your" troubles instead of "his" troubles, since it refers back to Hamlet.

Overall, these sentences are quite well-written. I hope this helps!