I want you to ask about a usage.

In the manuscript, there is a sentence “it has to be a mindful kind of patience, the kind that took me some years to master.” The point which I want to ask is what that’s usage of “the kind that took~to master” is. In the sentence, there is not a conjunction just only that. I always confuse when it is used in a sentence. And “ I have known very many of them, professionally and privately and, if I please, could relate divers histories,   good-natured gentlemen might smile, and sentimental souls might weep.”

Why is there “at” in this sentence?

Please help me.