This paper is a reference for a hands-on workshop where participants will make polyhedra out of balloons, and learn how to use balloons to demonstrate mathematical principals, from preschool (counting, shape recognition) to college level (graph theory, theoretical computer science). Balloons are a great medium for teaching hands-on mathematics, whether to young students, who are more open to the idea that an octahedron (for example) is a beautiful object if it is made out of a balloon, to adults, who can find an interesting challenge in constructing complicated models. Balloons are also inexpensive, easy to obtain, and easy to work with (once you learn the basics, which will be covered in the workshop), which combined with their hands-on nature and visual appeal make them a great medium for teaching and learning mathematics.