Generating functions are powerful tools for solving a number of problems mostly in combinatorics, but can be useful in other branches of mathematics as well. The goal of this text is to present certain applications of the method, and mostly those using the high school knowledge.
In the beginning we have a formal treatment of generating functions, i.e. power series. In other parts of the article the style of writing is more problem-solving oriented. First we will focus on solving the recurrent equations of first, second, and higher order, after that develop the powerful method of "the snake oil," and for the end we leave some other applications and various problems where generating functions can be used.