Not for you eh

. Don't worry, I hear you. *wink*wink*
Ruby is another language, RoR is a framework written in ruby which provides premade objects which speed up development (similar to things like CakePHP or the Zend Framework in PHP).
Perl is yet another language, and one which pops up all over the place, it's generally used to manage/format/handle text etc, etc.
MySQL is an RDBMS (relational database management system) which uses the client/server model. You have the MySQLd (MySQL Daemon) which runs in the background on the server and does the database storage, searching, indexing, etc (see what a DBMS is for more info on what it does). Then you write programs which use client libraries to connect to the server and execute
SQL code on them to select, update, delete, etc information.
AJAX is nominally "Asynchronous Javascript and XML", but colloquially means anything in Javascript which fetches dynamic data (increasingly as JSON as opposed to XML) and uses something like the Document Object Model to dynamically place it in the layout without any page refreshes.