jQuery : jQuery is a fast, small, and feature-rich JavaScript library.
jQuery

Overview
jQuery is a fast, small, and feature-rich JavaScript library. It makes things like HTML document traversal and manipulation, event handling, animation, and Ajax much simpler with an easy-to-use API that works across a multitude of browsers. With a combination of versatility and extensibility, jQuery has changed the way that millions of people write JavaScript.

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Features

Lightweight Footprint
Only 32kB minified and gzipped. Can also be included as an AMD module

CSS3 Compliant
Supports CSS3 selectors to find elements as well as in style property manipulation

Cross-Browser
IE, Firefox, Safari, Opera, Chrome, and more