"Zepto is a minimalist JavaScript library for modern browsers with a largely jQuery-compatible API. If you use jQuery, you already know how to use Zepto.
While 100% jQuery coverage is not a design goal, the APIs provided match their jQuery counterparts. The goal is to have a ~5-10k modular library that downloads and executes fast, with a familiar and versatile API, so you can concentrate on getting stuff done.
Zepto is open source software and is released under the developer and business-friendly MIT license."
Note: jQuery appears to have better performance.
On the other side, both jQuery and Zepto.js are much slower than direct access to DOM from JavaScript.