The Rules module is an engine which allows site administrators to automate actions to be conditionally executed, either programmatically or in response to predetermined events.
Rules can react to Rules Events occurring on a Drupal site, such as a user logging in. And it can perform customized follow-up Rules Actions, such as redirecting to a certain page, which are to be conditionally executed if some Rules Conditions are satisfied.
Video tutorials: Johan Falk did an amazing job in the early Drupal 7 days by creating an impressive set of tutorials to "Learn the Rules Framework" with a set of over 30 videos and related blogposts hosted at nodeone.se
(license = Attribution-Noncommercial-Share Alike 3.0).
However the nodeone.se domain is no longer hosting them. Learn Rules is an attempt to recover these valuable blogposts (with related links to the corresponding videos).
The Tiny Book of Rules is a (15 pages) jumpstart about the Rules module.