The "social leap" in the book's title refers to the solution that our ancestors came up with when they left the rain forest for the savannah. The book describes the benefits, challenges and tragedies of human sociality. The social capacity is based on collaboration, and we as a species are extremely dependent on working together. Many findings from recent research are brought together in an overview of the evolution of our ancestors. One example of how seemingly irrelevant findings can assist in figuring out details of our history is the evolution of a species of lice that requires clothing to thrive, genetically estimated to have occurred at about 70,000 years ago, gives an indication of the latest date when clothing became ubiquitous.
An important theme is the fact that evolution cannot produce clean-cut solutions to many conflicts or discrepancies between possible strategies for survival. Very often, almost always, some strategies become dominant, others recede in importance, but are often still stably present, as the ecological situation for a species change. There are complex feedback loops, where a particular evolutionary invention causes new challenges. So it was with human sociality. It solved a problem, and produced many new ones at the same time.
The book narrates the story from the Oldowan stone tools made and used by Homo habilis about three million years ago, via the more advanced Acheulian stone tools made by Homo erectus one million years later, to Homo sapiens about 300,000 years ago. The themes include fire, migration, farming, theory of mind for social learning, cities, hierarchies, and many more. An important point is that although we may be considered the ultimate innovator of the animal kingdom, it is sufficient if only very few people actually make new innovations. Our cumulative culture, where new, useful innovations can spread and be transmitted from generation to generation. The people doing the transmitting may not even be aware that they are selecting the best innovations, it's just part of the logic of evolution that this can happen if the circumstances allow it.
There are too many themes discussed in the book to bring up here. However, although culture is discussed, the interplay between sociality, culture and norms could have been more deeply analysed. A number of interesting examples are presented, but a rounded discussion is lacking.
The final part of the book discusses happiness, and proposes that evolution didn't design us to be happy, but rather to wish to be happy, and occasionally achieving it for short time. If we were too happy, we would just lie about and do nothing, thereby not procreating or surviving in sufficient numbers. It's a provoking thought which in itself makes it worth reading this book.