1. I don’t read a lot of non-fiction books, not because I don’t start them but because I don’t finish them. Most aren’t good or important enough and you are often better off reading the blog post or HBR article on which they are based. So you may want to take my claim of “one of the best” with a grain of salt but I don’t say it lightly either.
2. Taleb’s writing can be annoying as it is sometimes comes off as arrogant or grandiose. Don’t let that stop you from reading Antifragile. He has something extremely important to say and it is well worth getting past style and ego. My advice: simply treat occurrences of “I am smarter, better read, more buff (just short of and have better sex) than you the reader” as entertaining. I should add: all of the aforementioned are potentially even true which might make them more rather than less annoying.
3. At varying points, Taleb overstates the strength of certain claims. Again, I suggest you don’t let that stop you. I can’t quite tell whether he does it because he genuinely believes it or because his interpretations are so counter to the received notions on these points that he feels he has to take an absolute position to make it stick (see footnote ). It doesn’t matter because throughly exposing yourself to his views will give you a much better understanding of the world.
4. Most importantly, please ignore anyone who claims that Antifragile is based on faulty math. The heart of the book is not based on complicated math but instead on a powerful logical argument. Formulas would be a distraction from the power of this argument instead of strengthening it. For those who really care about math there is a separate mathematical document freely accessible on the web (I am still working through it and don’t expect to finish that until the summer). Rest assured though you can safely ignore it and should be very skeptical of anyone claiming to use math to counter Antifragile.
So with that out of the way let me try to summarize the essential line of argument from Antifragile.
1. Some things are fragile, which means they break under stress. If you pick a glass vase off the floor and drop it, it will break, i.e. be worse off. Other things are robust. If you pick up a rubber ball off the floor and drop it, it will bounce instead of break and so will be unchanged. But there is yet another category and it is things or systems that are anti fragile. If you yourself jump off the floor and land again your legs are becoming stronger. Stress (within certain limits) is in fact good for the body. The body is thus more than robust, it is antifragile.
2. The world is full of non-linearity. There is a height from which you can drop the glass vase and it won’t break. But just above that it will break and the two outcomes are entirely different. The damage to the vase is not proportional to the height of the drop. The same can be true for upside. One example are successful investments in network effects businesses such as Tumblr. The value of the network rises far faster than its size. When things are non-linear relatively small changes can have a large impact on the outcome. Importantly what matters to you is the outcome, not the variable.
3. The past is a fundamentally flawed predictor of the future. I really mean fundamental here. There is no amount of mathematical sophistication that will fix this problem. Why? Extreme events are underrepresented in the past. They have to be. Axiomatically so. To see this consider the real extremes. Events in which the earth is destroyed are underrepresented because otherwise you wouldn’t be reading this. Similarly, events in which we have figured out how to feed information directly into the brain of every human haven’t occurred yet because again you wouldn’t be staring at a screen or printout right now. I made this argument at the level of the whole planet / all of humanity where it is easiest to see but it applies equally at smaller scales such as the economy or even a single company or individual human being (or specific glass vase). It also applies to less extreme outcomes than the ones I chose. For instance, the largest previously recorded flood is an upper bound on the floods for which we have past data (by definition) and even larger floods are completely absent from the data (but that does not make them impossible) 
Now all you have to do is put these three arguments together and you get to the heart of Antifragile, which is as follows:
A. Because of #2 and #3 proper predictions about the future are hard (thanks Yogi Berra) and therefore you are better off working on #1, i.e. being antifragile than investing in complicated mathematical models (that don’t work)
B. There is a specific way to be antifragile: avoid situations with limited upside and very large non-linear downside which are “sucker’s bets" and instead seek situations which have limited downside and very large non-linear (ideally uncapped) upside. 
This applies to how we live our lives as individuals, it applies to companies, it applies to governments and even the human species at large. Much of Antifragile examines different areas of life such as education, medicine and government and analyzes them in this framework. This turns out to be powerful as it shows that much of what ails us can be comprehended and potentially fixed by moving from fragility to antifragility (and by detecting where someone has made themselves antifragile at the cost of others). I won’t attempt to summarize or review those applications. Each one of them is well worth the time reading.
Bottomline: finish whatever book you are currently reading (assuming you like it) and then read Antifragile next.
 It is in some of the applications where Taleb overstates his case. For instance he takes an extreme position on the relation of theory and practice arguing that practice informs theory and not the other way round. While I agree entirely that the theory to practice direction is vastly overstated, “in practice” the two inform each other and trying to pin down causality strictly in one direction seems futile. Looking at computer science, a domain that I know something about, he is entirely right that many and possibly most important contributions have come from practitioners. But there have also been huge theoretical breakthroughs in information theory and cryptography that have provided the basis for practical work at a completely new level. Write theory and practice on two sides of a strip of paper and then fold and glue into a Mobius strip and you have a better model of the interaction of theory and practice. Addendum based on a tweet by Taleb: here is a piece in which he states the argument less strongly as “Theory is born from (convex) practice more often than the reverse (the nonteleological property)” (emphasis mine). That I agree with and I will reread the chapter in the book and potentially replace with a different example.
 So you might ask: I buy the argument for the really extreme outcomes but can’t we make use of the data on the somewhat less extreme outcomes? The first answer is: it’s the really extreme outcomes that matter the most, so this question is less important than you think. The second answer is: this is where you should consult the mathematical part if you really care as it shows how for combinations of non linear effects with naturally occurring fat tail distributions you can get (arbitrarily) large prediction errors (on the outcome, which — keeping #2 above in mind is the thing that matters)
 The non-linearity of the payoff function for the “sucker’s bet” is concave whereas the one with the dramatic upside is convex. So you can restate the rule as: avoid concave non-linearity (which is fragile) and seek convex non-linearity (which is antifragile). Footnote added per Taleb’s tweet.