2 Samuel

I have a question for anyone out there that can provide insight to me. As I read along with 2 Samuel, this book seems to mainly reference King David. I participated in a Bible Study class at church which gave us the story of the Old Testament.
I remember reading about David as one of the Figures in the Bible and the Era was the Kingdom Era...so is the book of 2 Samuel associated with the Kingdom era?

Also, the storyline was summarized for us which stated: "David, the greatetst King in the new monarcy is followed by a succession of mostly unrighteous kings, and God eventually judges Israel for her sin, sending her into exile."

Is this the same David in the book of 2 Samuel that they are referring to. Because David doesn't seem that "great" to me. There is a lot of wrong doing during his rule. If anyone can shed any light on this I would truly appreciate it.