Mandelbrot is an odd duck. He's a bit of an outcast from both the Financial and Mathematics communities (finance types didn’t like him because he focuses on obscure applied mathematics, mathematicians think finance types are focused too much on money and not enough on pure math).
Mandelbrot is most famous for coining the idea of Fractals; self-similar shapes which don't lose resolution as you zoom in or out. Good examples would be:
He devoted his life to studying this "roughness" in shapes and in nature. In addition to looking at 2d and 3d space, Mandelbrot argued that this "roughness" coefficient should be an extra dimension to look at various patterns, even in 2d space.
The book takes this thinking and applies it to economics. Mandelbrot's big argument is that the way we look at markets today is mostly wrong.
We tend to think of markets as "random walks". The price from one day to the next will follow some normal bell curve distribution, and either increase or decrease, but not wildly divulge from the mean. There's a whole host of formulae to describe the returns of markets in this way: Sharpe’s CAPM, Black-Scholes, etc.
Mandelbrot instead argues that all of these are wrong, because they don't empirically match the way that markets work. Instead, markets tend to cascade and jump wildly in spurts, much more than a random walk might predict. He argues that you instead of estimating in terms of random walks, one should look at the rate of change or the delta in markets. Within those deltas, you will find both fractal behavior and power laws related to it.
From looking empirically at Markets, it’s important instead to take in several ideas into account.
Overall, the book taught me quite a bit about how markets actually behave, when viewed from an empirical sense. If you like Taleb, or reading about finance in general I think you’d enjoy it.
Additionally, this has underscored my conviction that visualizing data can lead to deep levels of insight. Mandelbrot got his start by simply looking at shapes, and understanding their repeating, self-referential patterns. I think more fields could (and should) do the same. Data visualization is powerful!