This document provides an introduction to fractal geometry and its applications. It discusses how fractals were discovered by Benoit Mandelbrot and have self-similar patterns seen at different scales. Examples of fractals in nature are given like coastlines, mountains, trees. The key fractals discussed are the Mandelbrot set and how it is defined mathematically. Applications of fractals mentioned include use in special effects in movies like Star Trek, modeling weather patterns, landscapes, and more. Areas where fractals are found include astronomy, biology, chemistry, art, music and others.