Rating: 
Summary: Good as research reference, but not in mastering the field
Review: As a research economist or graduate student, especially if working in economic theory or dynamic macroeconomics, it is difficult to overstate the value of this book as a handy guide for a set of essential facts (re: theorems) regarding the existence of solutions to dynamic programming problems or markov decision processes, as well as characterizing the properties of the set of solutions.
That being said, this is not the book a budding theorist wants to learn techniques from (For the mathematical prerequisites: measure theory, topology, probability, stochastic processes, hilbert spaces, there are better treatments in the math literature. For dynamic programming in discrete time itself: Bertsekas and Shreve's 1978 text is far superior). Though I am not an expert in macroeconomics, I believe Sargent's sequence of books is a better source for learning the how-to-do, while keeping the economic questions crystal clear: neither of these is a strong point of this book.
Rating:
Summary: Too Minnesota
Review: Covers some good material needed for modern macro analysis, but gets so excited about the math that it forgets to actually do much economics. This book may be mainly authored by Chicago types, but it is Minnesota to its core. Yuck.A good book if you think you are smarter than most and like to show that off. A bad book if you like to do economics and want to see the payoff that actually (really!) can result from learning some reasonably complex math. But I do conceed, can be a useful reference and despite all the greek, a few interesting points fall out in between the equations.
Rating: 
Summary: Essential
Review: Essential for understanding modern macroeconomic theory, for better or worse. Chapter 4 on Dynamic Programming under certainty and bounded returns is beautiful. I recommend using this book in conjunction with Sargent's RMT.
Rating:
Summary: A book in need of a study guide.
Review: First, let me say that this is an IMPORTANT book; about as important a book on macro that has come out in the last 30 years. That said, it is a horrible book to learn by. It should not bill itself as anything other than a reference book. It doesn't have any examples; just a lot of exercises. By trying to be general, it leaves the beginning student without a clue as to how to apply this in a more concrete context. In short, if ever there was a book in need of a study guide with examples worked out, this is it.
Rating:
Summary: The best math economics book I've ever known.
Review: For those who want to have an idea of the math level required by modern economics Stokey and Lucas' book is a must and has no competitors (it comprises material taught only at Math courses for Mathematicians and Physicians, and now for Economists). Takayama's is out, and Sotkey and Lucas' is in. Warning: Modern economics is terribly abstract.
Rating:
Summary: Essential for doing modern macroeconomics
Review: If you want to do modern dynamic models of macroeconomics, and need the basic tools, this is an essential part of the toolkit. The book has been out for a while, and there have been developments in the field that probably need to be in the next edition. But it does present the basics of what could be described as the CarnegieMellon-Minnesota-Chicago approach to modern dynamic macroeconomics developed by Lucas and Prescott in the early seventies, the work that led to the Rational Expectations Revolution and current work in Real Business Cycle Theory. This is what you need to read papers in Econometrica or the Journal of Economic Theory. This is a standard graduate macroeconomics text. Some reviewers have criticized it without fully understanding the objectives of the authors. For instance, read Chapter 5, with its careful, and explicit examples of how to use these methods in constructing simple and parsimonious models. Yes, some of it is a rehash of standard theorems in dynamic programming, and measure theory, and so on, but the goal was to provide these in one location, so that you don't have to learn these by digging through the appendices of Bob Lucas' papers, or the first 100 pages of Dunford and Schwarz's Linear Operators or Halmos, or the Annals of Mathematical Statistics where Blackwell published the results that are now used. I would recommend Sargent's books as an useful accompaniment, and also perhaps the Exercises by Sargent and Manuelli.
Rating:
Summary: A book in need of a study guide.
Review: It's a very difficult book to understand, if you do not have an excellent background on stochastic process, markov chains, vector space optimization, etc. I did not find it very useful.
Rating: 
Summary: Very difficult for a first course in economics dynamics
Review: It's a very difficult book to understand, if you do not have an excellent background on stochastic process, markov chains, vector space optimization, etc. I did not find it very useful.
Rating:
Summary: Classic Textbook on Mathematics for Economists
Review: Let's get three things straight. This book is (1) a textbook, (2) in mathematical techniques, and (3) aimed at economists. As a textbook, it contains a large number of exercises with which students can test their understanding. As it is written for economists, it is not as rigorous as a mathematics text, but is pitched at a level of rigor appropriate for an economics graduate program at a school like Chicago. As it is a mathematics text, it does not emphasize the economics underlying the problems. Given this, I think the book does a wonderful job. It is beautifully intuitive, illustrated with lots of examples, and is just rigorous enough to provide the grounding necessary to go on to more advanced mathematics texts. And for those who want a solutions manual, one is on the way ... Harvard University Press expects to release one some time in 2002. Early drafts are available from the authors: Irigoyen, Rossi-Hansberg and Wright, who are all graduate students at Chicago....
Rating:
Summary: Hamiltonian Hills
Review: My first thought upon encountering this text was "man, this book is really green". However, that was probably due to my problems with dichromatism. Once inside, I was convinced that the authors and their school of thought have taken the field of economic jestership to new heights. However, I had to go back outside for some fresh air, and I haven't been back inside for a while. It's too nice and sunny, you know. Join me as I prance naked over the golden hills, my life unencumbered by the patronizing utterances of uncouth ungulates, my mind filled with daffodils instead of dynamic optimization techniques, my schlong swinging in the succulent seabreeze! Your brain is a bouquet, not a black box of baneful baloney! The horizon is not infinite! Set your discount factor to zero! Wohoo!!!
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