Eli Bendersky's website Jared Diamond is well known through his later, Pulitzer prize winning "Guns Germs and Steel" (GGS). "The Third Chimpanzee" is an earlier book from 1997, where Diamond mixes some precursory ideas for GGS, with some chapters that would later appear in full light in "Collapse", and with a well-told account of the human race evolution, and evolutionary psychology in particular.
The first part is a lighter, more popular-oriented account of other, more serious works on genetics and evolution. I found this part occasionally lacking in rigor and even mistaken in some places, especially compared with Dawkins' books. One example is a long discussion of how people and other animals pick their mates. Diamond raises several questions, tells of some interesting research, but eventually leaves the riddle unsolved. This is quite weird, because geneticists have explained the mechanism of mate-selection years ago, reasoning that it's our genes that try to find genes similar to themselves in the mate, in order to propagate with higher certainty. Generally, the gene-oriented view of evolution, which emerges as the correct approach in recent decades, somehow seems to elude Diamond, who still appears to be convinced in the mechanism of organism selection. For example, here's a quote (p. 127, paperback edition):
[...] The complication that makes these evolutionary design problems less simple than they might at first seem is this: natural selection acts on whole individuals, not on single parts of the individual.
Whoops! Unless it can be excused as an over-simplification, this point is a gross mistake given all the recent research results! Natural selection acts on genes, not individuals. Later Diamond even hints at whole tribe-selection, which is even farther from the truth. While tribe and individual selections are a good enough first order approximation to how the world works, once you want to understand complex phenomena, they're insufficient. Kind of like Newtonian physics, discarding relativity.
Don't take this to be a severe criticism of the book, however. Such mistakes are few and far apart in what is a generally good introduction to human evolution. Diamond has a knack for talking about complex topics in an entertaining manner, providing a lot of interesting research results that corroborate the theories he explains. The rationalization of aging is particularly good, and well worth reading and understanding.
Later come some interesting general chapters dealing with the uniqueness of the human race in the world. There's a great chapter on human language, and then chapters on art, agriculture, drugs and aliens.
The second half of the book, as I've mentioned earlier, is pretty much a prelude for Diamond's later books, GGS and Collapse, so if you've read those you won't learn much new. But if you didn't, it can serve as a very good 150-page introduction to the topics Diamond spends 900 pages explaining in his later works.