Comparison of 20 javaScript frameworks: jQuery is the most popular JavaScript library

jQuery is a JavaScript library designed to simplify the client-side scripting of HTML. jQuery is the most popular JavaScript library in use today (used by over 43% of the 10,000 most visited sites).

site: http://jquery.com/

--------ABOUT BROWSER COMPATIBILITY

http://docs.jquery.com/Browser_Compatibility

-------USE:

It can be included within a web page by linking to a local copy, or to one of the many copies available from public servers such as Google:

load request: google.load("jquery", "1.6.1");
path: https://ajax.googleapis.com/ajax/libs/jquery/1.6.1/jquery.js

http://code.google.com/apis/libraries/devguide.html#jquery

The Google Libraries API is a content distribution network and loading architecture for the open-source JavaScript libraries. Using thegoogle.load() method gives your application high speed and global access to the open-source JavaScript libraries.

A basic introduction to jQuery and the concepts that you need to know to use it:
http://docs.jquery.com/How_jQuery_Works

-----Comparison of  20 javaScript frameworks:

http://en.wikipedia.org/wiki/Comparison_of_JavaScript_frameworks

Ally

Ample SDK

DHTMLX

Dojo

Echo3

Ext JS

Google Web Toolkit

jQuery

midori

MochiKit

MooTools

Prototype & script. aculo.us

Pyjamas

qooxdoo

Rialto Toolkit

Rico

SmartClient & SmartGWT

SweetDEV RIA

YUI

ZK
-------list of google.load javascript libraries:

  google.load("dojo", "1.6.0");
  google.load("ext-core", "3.1.0");
  google.load("jquery", "1.6.1");
  google.load("jqueryui", "1.8.13");
  google.load("mootools", "1.3.2");
  google.load("prototype", "1.7.0.0");
  google.load("scriptaculous", "1.8.3");
  google.load("swfobject", "2.2");
  google.load("yui", "3.3.0");
  google.load("webfont", "1.0.19");