This week's book giveaway is in the OCAJP forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide 1Z0-808 and have Jeanne Boyarsky & Scott Selikoff on-line! See this thread for details.
Even though it's getting a bit old, Ajax in Action is still relevant when it comes to learning the basics of Ajax. Though its use of Prototype is rather creaky (Prototype is a bit of a dinosaur these days).
There'a also Head First Ajax (which I helped to review) which is very good if you like the Head First style.
And once you want to start using it for real using jQuery, I recommend by own book (of course): jQuery in Action; chapter 8 is completely devoted to Ajax.