If you don't already know JavaScript, and probably even if you do, Douglas Crockford's videos are awesome. He also covers the DOM, which is intrinsic to working with AJAX.
Start with "The JavaScript Programming Language", and then do "Advanced JavaScript" and finally "An Inconvenient API: The Theory of the DOM" (the latter two can stand alone, and if you're in a hurry, maybe get the DOM out of the way). That plus spending some time with Firebug and a few interesting JavaScript applications (and building some of my own) has been the entirety of my JavaScript education. I bought the "Definitive Guide" from O'Reilly, but haven't used it heavily.
There are other useful videos on the same page, including one with Joe Hewitt introducing Firebug. I can't stress enough how helpful Firebug has been in helping me learn JavaScript and AJAX.
Note that I haven't talked much about AJAX. AJAX is a tiny piece of JavaScript, but in order to build useful applications you need to know a lot more than AJAX. So, learn JavaScript and AJAX will come naturally.
As others have mentioned, the good frameworks make dealing with browsers easier, since it hides compatibility issues as well as some of the complexity. Mainly a framework just allows you to spend more time thinking about your specific needs rather than the tedious plumbing work of getting stuff happening on the page.
Oh yeah, +1 Firebug. You need Firebug. Figuring out WTF is going on is nearly impossible without it, unless you're a masochist and enjoy debugging via alert dialogs.
http://developer.yahoo.com/yui/theater/
Start with "The JavaScript Programming Language", and then do "Advanced JavaScript" and finally "An Inconvenient API: The Theory of the DOM" (the latter two can stand alone, and if you're in a hurry, maybe get the DOM out of the way). That plus spending some time with Firebug and a few interesting JavaScript applications (and building some of my own) has been the entirety of my JavaScript education. I bought the "Definitive Guide" from O'Reilly, but haven't used it heavily.
There are other useful videos on the same page, including one with Joe Hewitt introducing Firebug. I can't stress enough how helpful Firebug has been in helping me learn JavaScript and AJAX.
Note that I haven't talked much about AJAX. AJAX is a tiny piece of JavaScript, but in order to build useful applications you need to know a lot more than AJAX. So, learn JavaScript and AJAX will come naturally.
As others have mentioned, the good frameworks make dealing with browsers easier, since it hides compatibility issues as well as some of the complexity. Mainly a framework just allows you to spend more time thinking about your specific needs rather than the tedious plumbing work of getting stuff happening on the page.