Ok, this was a long and tedious book. It was cumbersome to finish it without falling asleep. Even though the author bases his analysis on data, for some reason, he also decided to use fiction novels as sources of information. Maybe he did so to make the book more appealing to a general audience — but I doubt that a broad audience would enjoy the manuscript even with this addition.
The basic idea that the author presents is the following: economic inequality rises (the book hit shelves in 2013) — and one of the main culprits is the difference between income on capital and income on labour. Thomas claims that the wealthy get wealthier faster than workers who only rip the rewards of their work. The argument is quite logical: if you have $100M in your bank account, it's easier to become the next richest person on Earth than if you don't have $100M.
Chuck Collins discussed the issue of growing inequality due to the growing chasm between returns on capital and returns on labour in a somewhat more exciting way in "The Wealth Hoarders." I recommend reading that book as a prerequisite. Actually, first, read the summary by Justin Fox, then the whole Wikipedia page (including criticism) — and only then proceed to the "Capital in the Twenty-First Century" if you still have the will to dig deeper.
The solution? Tax the rich. No, seriously, if you tax the wealth of the wealthiest people, even by 2% of their whole net worth a year — they won't notice it. Yes, their wealth accumulation will slow down, but considering that they already have more money than they can spend, the change for them will be unsubstantial.
Whether this solution would work or not is up to debate — yet I think this solution is the best we can get in our ever-changing, complex world. Whatever complex solution we try to implement, there will be ways around it — and the wealthiest people will exploit them. The solution must be simple enough to avoid any loopholes.