In his play Hamlet William Shakespeare was presenting a new story in a traditional genre - the revenge play. There had been one or two stories with this theme before, but Shakespeare chose to focus in very closely on the effect of vengeance on the individual, in this case Hamlet himself.
At the beginning of the play we see Hamlet as a young man facing the future as a man uncertainly - there's nothing new in that. But this young man has additional issues and burdens to cope with before he even starts out in life. At the beginning of the play we see him full of self doubt. He gradually moves through despairing emotions and angry moods (you could find quotes to illustrate each of these three) and then verges on the suicidal. Gradually his idea of "self" is being destroyed and this is mirrored in social decay around him. One plan he feels duty-bound to follow but the other is to go with his gut feelings.