Recently I got the book "Dart: Up and Running" written by Kathy Walrath and Seth Ladd. Both authors are well-known in the Dart community. Kathy is responsible for so much great docs on dartlang.org and Seth was the Dart-Ambassador since the language first faced the world (or even earlier, who knows). Definitely you want to meet at least one of them in your favorite coffee shop when you are running into Dart related trouble.
The Book itself is one of the first of its kind. Currently I know about two more Books on Dart, but that's it. As the language still progresses and changes are flowing in every day, it is a difficult matter to write a books about Dart. Kathy and Seth decided to write a short but valuable book, tailored for the busy developer who wants to get an overview on the Dart eco system. With that in mind most of the content will be valid for quite a while.
Actually you can read everything you need to get started quickly. After a brief introduction of the "whats hot" kind you'll be introduced into the Dart syntax. You'll see a lot of the great language features Dart supports, like named Constructors or the Cascade Operator. The second chapter is a tour through the current Dart libraries, like for working with Isolates, HTML manipulation or I/O. It is a brief read which shows you what you can do with it, but doesn't exhaust all possibilities. Of course a chapter on the great Dart toolset is not missing. If you ever wondered why people are so excited on Dart, this one of the reasons: the Editor and Dependency Resolver (aka Pub) is already built-in. The chapter introduces all of them and points you into the right direction when you are just starting. Finally the book ends with an example chapter.
This book is one of the kind you need to have on your desk until you know it from mind. It is an easy to read, easy to understand book which helps you to get started quickly. Don't expect Kathy & Seth will explain object oriented paradigmas to you: it is really focused on the language itself.
If you are curious and would like to read more on the book I have some good - no GREAT - news for you. The whole book can be read online and free of charge. Just head on to the "Dart: Up and running website" and start hacking today. I also would like to mention that the books text and all source code examples are available on GitHub. You see, there is no excuse anymore. ;-)