The ideas in this book are probably not news to artists, but they were new to me, so it was instructive. But, even though it's a short book, he explains things to death. There was *lots* of repetition of the same basic idea.
The basic idea is that when you mix blue and yellow, they don't always make a nice, clear green as you might expect based on what you were taught in school. You might end up with a muddy brownish olive instead.
The reason that might happen is because no paint color is true blue, yellow, or red. All yellows are either greenish or reddish; all reds will be either bluish or yellowish; and all blues will have either a yellowish or reddish cast to them. If you mix blue with a reddish yellow, it's almost the same as if you mixed in a little red along with the blue and yellow, so you come out with a muddy greenish color. To get a nice, clear green you have to mix the blue with a bluish yellow. And the same for the other colors. A yellowish red mixed with a reddish yellow will give a clear orange; if you use a bluish red or a bluish yellow, or both, the color will be more subdued and brownish. According to the author, you mostly only need six colors -- two versions of each primary color -- to mix just about any color you want to use, so you can save a lot of money by not buying colors you don't need. Once you read this basic idea it seems obvious, like something you probably should have been able to figure out.
That's not the only idea in the book; the author does tell a little bit about what color names or ingredients tip you off as to whether you've got a bluish or a yellowish red, for example, in case you're not good at figuring it out. And he talks about which pigments tend to be higher quality, which tend to be more opaque and which transparent, and which colors other than the primaries might be useful and why. Still, some of the Amazon reviews I've read cite books on the same topic that are supposed to be better, those might be worth checking out. I might take a look at "Color Choices" by Stephen Quiller and "Color Right from the Start" by Hilary Page.