Wait a minute: has violence declined? The first 361 pages argue that it has. A significant decline since records began; all forms that can be measured: murder, rape, war, etc. You might be thinking: wait a minute, World War I, World War II?! This is where you might disagree with what Pinker means by "violence has declined". He means the rate has declined, not the total number of people dying from it. A war that killed 2 million people back in the 8th Century, Pinker says, is much worse than a war that killed 2 million people nowadays, because there was less people then (it killed a larger percentage of the world back then). Get it? So taking the world population in consideration, Pinker is definitely correct that the rate of violence has gone down (all his graphs show a steep decline from top-left to bottom-right). In other words, if hypothetically you could pick any time period to live in, you may want to pick now because overall you have the least probability of dying from violence (unless you get dropped in Wash. DC!).
Another piece of his argument is to say that many forms of violence have been simply eliminated; no more witch burning, no nukes have been used, no great powers have fought since 1953, slavery has almost been eliminated, and so on. There's a whole new moral consciousness, caused by numerous developments (social, political, economical)--it's not that human nature changed.
Some people are a little worried about Pinker's arguments because they sound "old fashioned"; a little "arrow-of-history-ish" (history is pointing us towards some goal) which has a bad track record; or they sound a little ethnocentrist (civilized people are way better than primitive people who live in a state of war constantly); or a little democracy-biased. Plus I bet some historians are saying "who does this linguist think he is!" He is aware of these concerns, which is part of the pull to read the book (and watch his youtube videos).
Whether you have reservations or not, this book is an enormous endeavor, an audaciously large project that I cannot help but appreciate as such. It's part of a new trend to "mathmatize" history, using numbers to tell the story. I am amazed that one man could write on so many topics, pulling from so many sources. And it helps that Pinker is a master at writing good sentences that flow. There are hundreds of talking points. If you like history and evolutionary psychology, I recommend this book especially (oh did I mention it's really long?).
Better Angels of our Nature