This book is the result of Don Topkis's original work on submodularity theory. As often occurs in original work, the inventor is not able to explain its structure in the most intuitive terms.
That being said, this book is a valuable reference to all who are using submodularity theory in research.
I think this theory is is probably the most significant contribution to optimization theory in the years after Danzig, Kuhn-Tucker and Rockafeller. Give the guy a hand!
useful to have at hand2008/11/30
This is a survey of (all?) results in Supermodularity Theory up to the 1990s. It is self-contained but does not provide much intuition (personally I got more intuition in the chapter devoted to this topic by Vohra). I think it is a useful book, but slightly overpriced - I got it on a discount.
Comprehensive and mathematically rigorous2000/12/23
Supermodularity and complementarity is an often overlooked area in economics and optimization. Few books devote any time at all to this subject (for a brief and simple coverage of the topic see book by Sundaram "A first course in optimization theory"). Topkis provides a self-contained treatment of this important area of knowledge and gives many new theoretical tools that must be a part of any mathematical programming or game theory course at a graduate level.
DO NOT BUY THIS BOOK2005/5/27
This book will only be useful to you if you already know about lattices and complementarity. It will not be useful to you at all if you are trying to learn about them. Most of the proofs are unclear and often are incorrectly referenced. There are also many questionable steps in the proofs as well as some typos. If you can't find anything better to learn from, I guess you have to buy this book. But avoid it if you can.