In Hamlet, in the soliloquy that starts with "O that this too too solid flesh would melt," who is Hamlet's anger aimed at why?

The anger in this soliloquy is directed mostly towards his mother, in frustration over her marriage to his uncle.  Hamlet's father had died just two months earlier, and already Gertrude had remarried, to Hamlet's uncle Claudius.  This occurrence is mortifying to Hamlet, incredibly depressing, and incenses him.  He feels that his mother is weak, inconstant, violating his father's honor and memory, and he is angry about it.  He doesn't understand how his mother could

"hang on [his father] as if increase of appetite had grown by what it fed on:  and yet, within a month"

had strayed from her love and married another.  She used to adore Hamlet's father, hang on him, worship and adore him.  And yet, it seems like it was all a ruse, because she so quickly tranferred her affections to another.

As the son of the dead king, Hamlet is furious that his mother would dishonor his father.  Her actions seem to spit on the memory of his father, tarnish his majestic reputation as a powerful king, and say a whole lot of negative things about the faithfulness of women in general.  Her actions make him declare with disgust, "frailty, they name is woman!" and turn against his mother.  Later, he lashes out in rage against her, and other women in his life.  I hope that those thoughts helped; good luck!