From where we can get more information about it.
In general search google for ajax. This ajax portal looks like it might be good.
Is AJAX mature enough to implement at production level.
Google certainly seems to think so. Personally I'd say if you're willing to either alienate your users with older browsers, or add in the compatibility code for them (hidden iframe, ala google suggests), then go for it. Of course remember to make it accessible to users without javascript too, unless you want to alienate them.