Galaxies are the fundamental units of cosmic matter that make up the universe and they change in remarkable ways over 13.7 billion years of cosmic time. We are just now discovering how galaxies we can see over these billions of years are evolving from small, star forming systems to larger, more massive and passive systems at later times. This book explains the structural evolution of galaxies, how we measure it, how these measurements change with time, and how observing this reveals important information about galaxy formation and evolution. It also explains the future of the field through the use of machine learning tools, and how galaxy structure can be used as a new approach to measure unique features of the universe, such as cosmological properties and parameters.