In Algebraic Geometry, one of the main objects of study is an "algebraic variety". One-dimensional algebraic varieties over the complex numbers are called "complex curves", and look to the naked eye like the surfaces in 3-space that are studied by undergraduates in Calculus. Complex curves are classified by an invariant called the genus, which measures the number of holes. The skin of a bagel is an example of a genus one curve. I'm going to introduce families of curves of genus g and, by giving lots of examples, motivate how one can learn about a particular curve by viewing it as a member of a family.