I haven't read any of Pinker's books yet. But I think this exploration of history of violence is an excellent intro to his advocacy. It is a chronological human progress towards global peace through various phases: the Pacification Process, the Civilizing Process, the Humanitarian Revolution, the Long Peace, the New Peace, and the Rights Revolution.
This is a great article that concludes Pinker's academic controversy and proposition in the midst of glooms (rising inequality, ecological catastrophe, etc). Some accuse Pinker as a defender of status-quo and intellectual service class.
John Gray criticizes Pinker's statistical numbers of his Long Peace idea. Gray says that "...while the seeming exactitude of statistics may be compelling, much of the human cost of war is incalculable. Deaths by violence are not all equal."