I'm about 100-150 pages into it, and I like this book. It's not for the faint of heart, however, and I haven't delved into much of the analysis and variations because I simply don't have the time. However, the book is quite readable, and Kasparov's effort of putting the games in context with a history and description of many of the many players and events surrounding the world champions is a welcome relief from the monotony of page after page of annotations and "informant" symbols found in comparable books of this level.
It should be noted however, that this book is not for junior students. In fact, I wouldn't recommend it to anyone under 1600 (perhaps even 1800), simply because there are other books out there that do a better job of catering to what junior players need to develop their game. That having been said, anyone who simply plays through the games and reads Kasparov's histories of the various world champions and their matches will be amply rewarded.
Some of the features of the book that I like:
(1) at the end of each chapter on each world champ, Kasparov summarizes with comments from other world champions regarding that individual.
(2) the moves to each game are printed in bold face so that it is much easier to distinguish the actual moves from the analysis.
(3) The analysis itself is insightful, and from what I have been able to ascertain, seems to be generally accurate. Of course, one should expect some errors as with any book. I'm not as much interested in variations and lines of analysis as I am in chess wisdom--general observations and maxims which I can put to immediate use--which is why I think that Bronstein's tournament book of Zurich 1953 is perhaps the greatest book on Chess ever written---certainly in the top 5.
(4) The language used in On My Great Predecessors is very well-thought-out and it's clear the writer took the time to express his thoughts precisely.
My chief reservation regarding this book is that it's difficult to tell what parts of the book Kasparov himself wrote (apart from the numerous "-G.K." quotes). I would like to think that Kasparov himself did a large part of the writing and analysis, or failing that, that he at least reviewed the analysis. It seems that the latter is true, although it's hard to confirm to what extent Kasparov himself was actually involved in the preparation of the text. It would have been nice if Kasparov's involvement had been clarified somewhere in the book. From the opening chapter where the author gives a one- or two-paragraph summary of each world champion, the author uses first person ("I see my style as...") when describing Garry Kasparov, suggesting that this paragraph (and perhaps that entire chapter) was written by Kasparov; however in the rest of the book the author attributes numerous quotes, including game analysis quotes, to Kasparov.
A comparatively minor issue is to what extent computers were involved in the analysis. A computer double-check is a good thing to have; however, anyone can load crafty or Chess Tiger on his PC and get good analysis from these 2600+ computer programs. In fact, the latest versions of Shredder are now over 2800! So when I buy chess books, I'm not looking for computer analysis but rather the insight---in English, not Informant symbols---which is unique to world-class players writing these books. However, it would have been good to see at least a blurb as to how computers were used in the analysis (e.g. what program, version, hardware, etc.).
In summary, from what I've seen so far, the book is destined to become a part of any Chess library, as important as the ECO's or ECE's. Once the whole three-volume set is out, it will probably become a standard reference work. I look forward to future volumes and editions.
This is a widely acclaimed book, it has generated a lot of fervor in the press.
I have had the book now for almost a month; it is no exaggeration to say that I could not put it down for the first two weeks or so.
I should inform you that it is an unfortunate fact of life that most of the (chess) books coming out of the old/former Soviet Union are "ghost-written" by minor players, trainers, etc. And if you check the dust-jacket, you will see that D. Plisetsky (and friends?) had a large hand in writing this book. And we are never really sure how much of the writing here is actually Garry Kasparov's work.
I hate to say it, but this book is positively riddled with errors. Kingston, Winter, and others have already pointed out numerous errors in their book reviews on the Internet - there is no need for me to delve into them here. (Except for the fact that Morphy did NOT "settle" in New York, as the authors here claim.) There are also MANY analytical errors, I found some in nearly every game that I examined!! For example: Take the game Pillsbury - Lasker; Cambridge Springs, 1904. After the move 21...Qc5!; we find the note: "But not 21...Rc8; 22.Qd4, Bc6; 23.Rxf6+!" The move ...Rc8; is one of the main tries here for Black. But 22.Qd4? is probably the SECOND or THIRD best move here. And 22...Bc6?? is simply a terrible move, it changes the computer's evaluations - FOR THE WORSE - by at least 5-to-10 points! (Forced was 22...Qd5; or even 22...Rxc4.) In fact the analysis of this encounter is SO bad, I only have to assume that the computer was not used ... or was turned off! (The publisher's website tells us every single move was meticulously computer checked, Kasparov himself affirms this in the intro/forward of this book.)
There are many other problems with this book as well. I would have expected to see all the best games of the four World Champions examined in detail - but this is not the case. Many of their losses are examined as well. In some cases you could say that the author was simply trying to be fair and that we are trying to get a balanced look at these players strengths and weaknesses. But in other cases, (Tchigorin - Gunsberg); I can find no relevant rationale for the inclusion of these games ... except that in many cases, these are famous games, and the author simply wanted to take a whack at them! (A definite lack of focus in a volume of this size.) Another major gaffe in a book of this size is NO bibliography. We may only scratch our heads and wonder at the author's sources. There are also ... TOO MANY QUESTION MARKS!!! I often wondered if Garry is even capable of being fair and objective - especially as concerns these older games. (How many of these new moves would have been discovered at all - except for the invention of the computer?)
By now, you might be thinking I hated this book. I actually liked it a lot. But I am just not sure if I can recommend this book to the average chess player, with the number of flaws that I know it contains. It is a real pity too, as with a little more work and some careful editing, this could have been a real landmark of chess literature.