questions about the Prolegomena

Hello,

I'm reading through the Prolegomena and I want to start this thread as a place to ask question about Kant's general philosophy.

First of all, there's this quote from the introduction:

"I therefore first tried whether Hume's objection could not be put into a general form, and soon found that the concept of the connection of cause and effect was by no means the only idea by which the understanding thinks the connection of things a priori, but rather that metaphysics consists altogether of such connections. I sought to ascertain their number, and when I had satisfactorily succeeded in this by starting from a single principle, I proceeded to the deduction of these concepts, which I was now certain were not deduced from experience, as Hume had apprehended, but sprang from the pure understanding. This deduction (which seemed impossible to my acute predecessor, which had never even occurred to any one else, though no one had hesitated to use the concepts without investigating the basis of their objective validity) was the most difficult task ever undertaken in the service of metaphysics; and the worst was that metaphysics, such as it then existed, could not assist me in the least, because this deduction alone can render metaphysics possible. But as soon as I had succeeded in solving Hume's problem not merely in a particular case, but with respect to the whole faculty of pure reason, I could proceed safely, though slowly, to determine the whole sphere of pure reason completely and from general principles, in its circumference as well as in its contents. This was required for metaphysics in order to construct its system according to a reliable plan."

I can't figure out whether he's agreeing with Hume and expanding upon him or rejecting his skepticism and offering a counterproof. What does he mean by "solving Hume's problem"? Does he mean to say that he figured out how we can legitimately deduce 'cause' and other such 'metaphysical' constructs exclusively through the understanding, thereby discreditting Hume's claim that it is merely a "habit of constant conjunction"?

It seems obvious that he accepts, like Hume, that certain concepts such as 'cause' are a priori (although Hume probably wouldn't have used that term) and "sprang from the pure understanding", but what isn't clear is what he means by "deduction" in the statement "I proceeded to the deduction of these concepts, which I was now certain were not deduced from experience, as Hume had apprehended, but sprang from the pure understanding." What is he 'deducing' exactly? Is he deducing which concepts spring from the pure understanding, and are thus a priori, or is he deducing those very concepts from the so-called "single principle", thereby demonstrating that there is only one a priori concept (if it is a priori) from which all others (like 'cause') derive?

These and other questions will surely follow.