This book aims to be useful to people of widely different backgrounds—from people with no previous experience in version control to experienced sysadmins. Depending on your own background, certain chapters may be more or less important to you. The following can be considered a “recommended reading list” for various types of readers:
The assumption here is that you've probably used CVS before, and are dying to get a Subversion server up and running ASAP. Chapters 5 and 6 will show you how to create your first repository and make it available over the network. After that's done, chapter 3 and appendix A are the fastest routes to learning the Subversion client while drawing on your CVS experience.
Your administrator has probably set up Subversion already, and you need to learn how to use the client. If you've never used a version control system (like CVS), then chapters 2 and 3 are a vital introduction. If you're already an old hand at CVS, chapter 3 and appendix A are the best place to start.
Whether you're a user or administrator, eventually your project will grow larger. You're going to want to learn how to do more advanced things with Subversion, such as how to use branches and perform merges (chapter 4), how to use Subversion's property support, how to configure runtime options (chapter 7), and other things. Chapters 4 and 7 aren't vital at first, but be sure to read them once you're comfortable with the basics.
Presumably, you're already familiar with Subversion, and now want to either extend it or build new software on top of its many APIs. Chapter 8 is just for you.
The book ends with reference material—chapter 9 is a reference guide for all Subversion commands, and the appendices cover a number of useful topics. These are the chapters you're mostly likely to come back to after you've finished the book.