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It kind of depends on what aspect of AIR you want to do. These days, AIR is primarily aimed at multi-platform mobile development. Although it could just easily be used to create desktop apps.
AIR will let you use the Flex framework, which uses Flash to build mobile apps. There are various good books there to get you started. Most Flex books will have a section on building an app with AIR. What AIR gives you is Flash outside the browser and access to more system level resources.
Flex 4.6 is the latest, but you would currently best be suited to looking up some online tutorials, as Flex just moved over to an Apache project. It won't change the basics, but I'm not sure what new components or interfaces may be introduced with that move. O'Reilly has a couple of Flex 4.5 for Android or iOS development books that cover some basics. They're mostly geared toward teaching Flex devs how to get their apps up on those mobile platforms rather than teach Flex development.
The Adobe video series on Flex in a week or something like that are still very good starting points. Hello Flex 4 from Manning is a very simple intro to Flex, kind of a Hello World for Flex, but was written while Flex 4 was still 'maturing' and most examples have some sort of errors.
Flex 4 In Action from Manning is actually pretty good. I liked it and covers Flex very well. Not much AIR stuff, but still a good Flex book.
O'Reilly has the Flex 4 Cookbook, which is a good reference, but not really a good learning book.
Overall, I think the Adobe resources are probably still your best bet to get up to speed quickly. If you are familiar with a C-style language, you should be able to get up to speed with Actionscript 3 (the language used for Flash/Flex) pretty easily. It's fully object-oriented and doesn't really have any quirks. Most developers complaints have to do with the Flex framework oddities, usually attributed to lack of being able to extend some components to their satisfaction.
I probably gave too much info, sorry. I'm primarily a Flex dev or should say, spent the majority of my time doing Flex dev.
tldr: Adobe tutorials are good starting points, Manning/O'Reilly books are good references.
Flex 4 In Action
http://www.manning.com/ahmed2/
Develop Android Apps with Flex
http://shop.oreilly.com/product/0636920020172.do
Develop iOS Apps with Flex
http://shop.oreilly.com/product/0636920021117.do
Adobe site for Flex tutorials
http://www.adobe.com/devnet/flex.html?view=gettingstarted