Lights Out is a simple electronic game containing a 5 by 5 array of lighted buttons.  Some of the lights are on, and some are off.  The goal is to turn off all the lights by pressing some sequence of the buttons.  Each time a button is pressed, it turns certain lights off and others on.  In this talk I will discuss how to solve the game, as well as some of the mathematics behind it.  It turns out that a thorough understanding of the game is equivalent to an entire undergraduate course in linear algebra!  While I will touch on this briefly, there will be little technical mathematics in the talk.  I will conclude the talk with a moral to the story, ie, a lesson which all those who would use mathematics to play games should know!