Like some others have said, this is a dissapointing book. What appeared to be a book that would bridge the gap between using JavaScript to perform DOM tricks and form validation and large AJAX applications turned out to be nothing more than a frantic overview of some of the core technology.
First and foremost, the pacing of this book is horrid. The obligatory "This is what AJAX means" introductory chapter is adequate, but things quickly go downhill from there. The next chapter, in which the author attempts to create a basic AJAX library, is confusing, largely because of the author's back-and-forth style. He spends more time rehashing and revising half-baked code than introducing the reasoning behind said code. This wouldn't be so bad if he summarized the library at the end, but instead he jumps right into a poorly described polling script. The author is anything but concise.
Second, adding to this frantic pace, is the author's penchant for glossing over important information. For example, loss of scope is (apparently) an important 'gotcha' to watch out for, but he never clearly explains where and why it happens. There's no real explanation of when executing context changes, or what it changes to (I'm guessing the most local scope, but who knows).
Regarding this, I must specifically mention the author's flippant use of object oriented JavaScript without any proper introduction to it. I'm familiar with using classes and objects in PHP and C++, but have never done so in JavaScript. The syntax seems straightforward enough, but his use of composition all throughout Chapter 3 may leave novices scratching their heads. Neglecting to use the UML to clarify his designs, especially in light of no OO introduction, was a horrible decision.
Finally, like another reviewer said, this book follows a pure step-by-muddled-step progression, so those readers hoping to skip to the good stuff will be disappointed to know that code in the later chapters relies on code created in the early chapters.
In the end, "Build Your Own AJAX Web Applications" misses the mark, and in a big way. The pace is frantic, the exposition muddled, and in the final tally, the book is best served being used as a coaster.