Many examples of fractal geometry are seen in the field of Astronomy, from nearby objects such as our Sun, to phenomena at intermediate length scales in our Galaxy such as the distribution of masers.  This talk will introduce fractal concepts and give many examples on various length scales - finally concentrating on the largest scales which can be probed in our universe, the analyses of galaxies.   This re-analysis of galaxy data, with methods that are particularly suited to fractal distributions, shows some surprizing results which are contrary to accepted ideas in modern cosmology.