In CPR here is what Kant says about Hume:

"David Hume, who among all philosophers came closest to this problem, still did not conceive of it anywhere near determinately enough and in its universality ... believing himself to have brought out that such an a priori proposition is entirely impossible, and according to his inferences everything that we call metaphysics would come down to a mere delusion of an alleged insight of reason into that which has in fact merely been borrowed from experience and from habit has taken on the appearance of necessity."

The "problem" Kant is referring to is how metaphysics can be possible in spite of what Hume proved. Kant says in the same breath, that this is the central problem of the critique - so i guess you can nearly say that it's written almost entirely as a response to Hume.

ooooh totally was. He was deeply affected by Hume's attack on causation, so tried to come up with a coherent response. Ended up positing a whole bunch of wacky and (I think) true things about our embedded cognition, so I think it's probably fair to say that Critique of Pure Reason is the result of his beef with Hume.