What is Hamlet's relationship towards Horatio, Ophelia and his mother?
Hamlet trusts Horatio above all the other characters in the play. Horatio is Hamlet's best friend, and the one that Hamlet relies on to help him see the reality of the situation with his father.
Hamlet's relationship with Ophelia is often debated, as to whether or not he truly loved her and why he treats her the way he does. The play seems to best support the idea that Hamlet did truly love Ophelia, but is disillisioned about love and loyalty through the marriage of his mother to Claudius. It seems that Hamlet doubts the sincerity of Ophelia's love for him, especially when she returns his letters.
As for Hamlet and Gertrude, Hamlet is deeply resentful of his mother's quick marriage. It is very clear that he is close to his mother, and that he esteemed his father above everyone else. While he knows that she was not immediately involved in the murder of his father, Hamlet equates remarrying with murder in Act 3 with the players. He judges her because of her fickleness, and this makes him suspicious of the integrity of others in the play.