Abstract: A powerful technique in minimal surface theory involves using meromorphic one-forms on a Riemann surface to prove the existence of previously undiscovered minimal surfaces in space. The one-forms are typically chosen to be compatible with a pre-existing visual image of the surface. Such images are quite common due to the development of computer graphics packages, and there are dozens of images of minimal surfaces available on the internet for which there is no mathematical existence proof. In this series of talks, we will define a minimal surface and discuss some examples, both new and old. Then, we will outline the technique of finding flat stuctures on minimal surfaces. Two particular flat structures will then be discussed in more detail in an attempt to show how broadly this technique can be applied. Finally, we will conclude with a specific application in an effort to communicate the mathematical ideas involved in an existence proof.