This is a good book as an introduction to the basics of New Keynsian DSGE models. Overall, it's a pretty good read, however it does have its flaws. The first one is that the book can be far too terse at times. Critical parts of the mathematical analysis are left out of the book. For example, you will not learn how to solve a DSGE model by reading this book. Nor will you learn how to estimate a DSGE model. You will not learn how to simulate a DSGE model by reading this book either. You will not learn how to check the stability of steady states. You will not learn how appropriate some of the quantitative methods used in this book, for example log-linearization, are. One could argue that the book was not written to teach any of these things anyway. The author's aim may have been to simply provide a brief, qualitative feel for how monetary policy models are constructed and what sort of insights they yield.
However, even by that goal, the book has some serious flaws. The author doesn't spend enough time in justifying some of the underlying assumptions that go into DSGE models, nor does he perform any sort of robustness check on these assumptions. For instance, after reading this book, I have no idea why Gali log-linearizes the first order conditions of his model before he proceeds to the solution. I know theorems like Hartman-Grobman allow linearization of the transition function in a neighbourhood of a hyperbolic steady state, but linearisation of the first-order conditions? Why is this legitimate? If so, HOW legitimate is it? Since we never actually get the solution to a real DSGE, we can't know how wrong the linearizations are. This issue is totally ignored by Gali. Likewise, what are the implications of the specific form of the utility function he picks for the agents(or should that be agent)? Why does the household have market power in setting its own wages? How robust is the numerical welfare analysis to a change in the underlying, arbitrarily chosen, welfare function? What are the implications of the outlandish assumption that there are an infinite number of identical countries each with measure zero? Why are we allowed to assume that the production function is linear in technology? Why do we use Calvo pricing over adjustment costs and what are the implications? Why do these models completely abstract away from capital and investment? Why is this legitimate and what are the implications? Surely a model studying interest rates should have meaningful investment/consumption decisions (in Gali's models, the representative consumer consumes all output in every period and there is never any savings, because capital is not required for production). These and many other pertinent issues are wholly ignored by Gali. He never indicates why many of the assumptions are made or what their potential consequences are.
Despite all these simplifications though, a lot of the analysis still ends up being numerical (rather than analytical), and I found this to be thoroughly disappointing. I can appreciate how such a heavily stylized model might tell you something qualitatively valuable, but I wouldn't put any weight on its quantitative predictions. As it turns out, the model's numerical predictions are basically all we get. After reading this book, I know vaguely *what* monetary theorists do, but I have no idea *why* they do it! Not only that, I wouldn't trust a DSGE model to tell me anything quantitatively relevant about the real economy.
On the plus side, Gali doesn't mince his words. The book is relatively short and it communicates its main ideas efficiently. This is in contrast to the excruciating exercise in verbosity put out by Michael Woodford.