In this first soliloquy Hamlet is lamenting the fact that God has a law against suicide. Hamlet is so devastated over his father's death that he has considered killing himself. He wishes that his "sullied flesh would melt, thaw, and resolve itself into dew" meaning he wishes he could turn into vapor and disappear. Life has become pointless to him. He cannot believe that, with his father only being two months dead, his mother has already remarried. What is worse Gertrude (Hamlet's mom) remarried Claudius (Hamlet Senior's brother and Hamlet Junior's uncle) only a month after becoming a widow.
Hamlet cannot believe his mother's choice to marry Claudius for two reasons:
1) Hamlet cites that his parents were so much in love. "Why she would hang on him as if increase of an appetite had grown by what it fed on" (Shakespeare Act I, scene ii 142-144).
2) Hamlet points out that even though his father and Claudius were brothers they were extremely different people. Hamlet states that comparing Claudius to his father is like comparing himself to Hercules. "My father's brother, but no more like my father than I to Hercules" (Shakespeare Act I, scene ii 154-156).
Hamlet blames his mother for her choice and says that it is not good. He also feels that nothing good will come of this marriage.