Chapter 1 answers the question "What is AJAX?" and gives a brief introduction and history lesson as to it's origins. This is very basic, but begins to get your feet wet understanding that AJAX is not a new technology - but one that has recently hit the spotlight.
Chapter 3 dives into the XMLHttpRequest object, its origins, and how to create a bulletproof instance of the object. This handles the differences between IE and other browsers and how they implement the request. He creates a wrapper for use (and use through the rest of the book) that allows us to send requests, receive responses, and then position it accordingly in the DOM.
Chapter 4 covers the Data Formats that are returned by our request. These include XML, JSON, and HTML. He covers each data format, and creates another wrapper for retrieving the different data formats.
Chapter 6 forces us to hit a wall (briefly). This chapter discussed the challenges that AJAX faces (and has faced in the past). Some of the challenges revolve around web services and connecting to remote API's, making your application backwards compatible, how to work around browser inconsistencies and consistencies (The back button and bookmarking), and how to wireframe an application that will change in each section.
Chapter 8 starts to wrap things up. Taking everything we have learned to this point, he discusses planning, applying, and bulletproofing your application.
Chapter 9, the final chapter, looks to the future of AJAX. Not only did it discuss the future - it covered many of the current frameworks available. He does a great job of discussing the good and bad of using frameworks - and where frameworks are best suited.