liby.js is a small JavaScript library with a focus on lightness and performance. Also, it is fair modular.
liby.js is by no means a framework, it only provides a minimum set of abstraction layers while allows you to use the native JavaScript and DOM as much as you love. The only exception is a compatibility layer for MSIE 8-9. This layer implements DOM Level 2 Events, Element interface (Element.prototype), and some other modern web standards, like a general purpose framework.
Most parts of the library is paranoidly tested with liby.js' own async test framework. This framework has no dependencies on liby.js and is able to power a server-side project (for ex. ngx_http_js_module).
liby.js powers such sites as Inshaker.com (now in private alpha, uses 0.4 development branch), Inshaker.ru (since 2007, uses current 0.3 branch), RetailStars.ru (since 2008, uses old 0.2 branch) and Programica.ru (since late 2006, uses ancient 0.1 branch). Yeap, all sites are in Russian. Please use Google Chrome translate functionality ;)