This book, in my opinion, is the most valuable book on dynamical aspects of the atmosphere insofar, especially from pedagogical point of views. As a foreign student, I understand well Holton's writings. Simple but very concise sentences, no wordy explanations. The first 3 chapters provide you the basic equations used in meteorology and their common approximations. The next 5 chapters, to me, are the most interesting chapters. They give you wide range of knowledge from boundary layer, synoptic scale phenomena, to instabilities. Equations are of great usefulness because THEY bring into the light physical contents of the dynamics of the atmosphere. To me, any analytical equation and its explicit solution provide us a more complete understanding than numerical models do (because you never know some unpredictable behaviour of numerical solutions). So, try to understand carefully the simplest cases that Holton selected. This gives you a lot of deeper understandings. Chapters 9 to 11 provide the dynamics of meso- to large-scale circulations. You will see why the Hadley circulation descends around 35N in very clear way. However, simple Poisson eqn with the argument of "positive forcing, negative solution" that is applied throughout the text should be paid especial attention because this conclusion is not always true. As a whole, the contents, explanations and derivations will be very well constructed if you see the main point of each section.
To get to the heart of this book, read and derive all the skips in Holton's derivations. The gaps are not too hard to fill out in math but require some thinking. DO ALL OF THE EXERCISES at the end by yourself and you will double your knowledge. For any math-related physical book, transparent derivations are the first thing you should figure out, physical explanations will follow subsequently. From my experience, people tend to skip any chapter what they thought they knew it already. If you apply this method here, you may be in trouble. Read carefully the first 5 chapters, understand approximations used in the each situation. Simply apply equations without judgments of their assumptions will take you into the nightmare.
I give this book 5 stars +. It is really classic....
