Homepage: http://www.yireo.com/software/labs/magento-api
This project includes a Joomla! plugin to load Magento code within Joomla! 2.5 or later. With this plugin, you can write PHP-code that refers to Magento classes and objects within Joomla! extensions. To use the plugin, install it in Joomla! using the Extension Manager, configure the Magento folder under the plugin-parameter "Magento root" and enable the plugin. Make sure the Magento folder is readable from within Joomla! (read-permissions, open_basedir setting, etcetera).
Joomla! 1.5 is not supported and never will be, due to incompatibile.
Disclaimer: Yireo is also the creator of MageBridge, which forms a bridge between Joomla! and Magento, and which main feature is to integrate Magento into Joomla! using an HTTP-based API. MageBridge is not needed to use this MagentoApi plugin. The only relationship between the two projects is that this MagentoApi plugin is perhaps used in MageBridge 2 as alternative to the HTTP-based API. This project will remain free as in speech and as in beer.
We have released an excellent guide for developing Joomla plugins: Programming Joomla Plugins written by Jisse Reitsma, a must-have for any serious Joomla developer.