Chapter 1: Getting Started
The book starts off with a quick introduction to jQuery, what it does and why it works so well. As the authors point out one of the great things you learn about jQuery right away is that it abstracts away browser quirks for you. With most browsers putting out a new version every few months this becomes a solid benefit for using jQuery.
The chapter finishes off with a quick mention and demo (using Firebug) of some tools you can use to help work with jQuery more efficiently when your writing code.
Chapter 2: Selecting Elements
Chapter 3: Handling Events
Chapter 4: Styling and Animating
This is probably the most fun chapter to read and work through the demos. You learn how to do animations (including custom ones) and effects. All the basics are here and are followed up with good demos and source code. In addition they show how to animate multiple properties at once (perhaps you want to use a slide and a fade effect together), simultaneous versus queued effect and ending off with working with multiple sets of elements.
Chapter 5: Manipulating the DOM
This chapter starts to get much more technical where you start to dive into doing heavier modifications like manipulating attributes (attr() and .removeAttr(), etc), creating/inserting/copying elements. Fortunately, the demos are great and present the content in a readable fashion that makes sense. This is a shorter chapter than some of the others but is packed with a lot of information. You might need to read it more than once to fully grasp it all if your new to jQuery.
Chapter 6: Sending Data with Ajax
Ah, AJAX! Perhaps one of the most discussed topics in jQuery books and articles for the past several years. No jQuery book would be complete without a discussion of the excellent support jQuery offers for AJAX. A simple example kicks off the chapter followed by loading JSON and XML content. Passing data to the server they show their demonstration and code using server-side PHP.
The section on Serializing a Form I think was good with the simple example they used but I do feel it should have followed up with a more real world example that was a bit more complex (using more then one form element, ex: using combo boxes, multiple textboxes, radio buttons, etc.).
The section Keeping an eye on the request is useful and shows you how to display a "loading" message wile your AJAX request is loading. They also show how to handle errors as well as security limitations which naturally leads right into a discussion of JSONP (JSON with Padding). The example is good and the typical warning on using JSONP is pointed out. The chapter ends with diving into the low-level Ajax method.
Chapters 7 and 8: Using Plugins and Developing Plugins
Both of these chapters are dealing with either using plugins or developing you own. Chapter 7 starts you off with locating, installing and using plugins. It ends off with one of the most useful plugin libraries available to jQuery which is jQuery UI. Also, as the book points out the jQuery UI library is really a set of plugins - you can pick and choose which ones you want in your project or take them all.
Chapter 8 goes over the types of plugins you can create and shows how to build each one. Both chapters give you enough to get started with plugins in general, at least to craft a simple to moderately difficult plugin. Its all the essential information you need if you do see yourself writing plugins in the future for jQuery.
Chapters 9, 10, 11, 12, 13
The final chapters in the book cover the initial topics but now dive deeper into them. Advanced Selectors and Transversing, Advanced Events, Advanced DOM Manipulation and Advanced AJAX are all covered and elaborated on.
This is an interesting way to split the book up with a great jQuery introduction at the start of the book and then diving deeper on each topic at the end of the book. Someone already familiar with jQuery could skip to the first half of the book when they feel they need more than just the basics. The same is true if your an expert in say AJAX but need to learn the basics of using plugins, etc. It makes for a great reference and a logical split of the basic information and the more advanced.
All-in-all this is a good book to learn jQuery with no fluff.