We will introduce the notion of formal group laws, which are power series somehow carrying the "essence" of a group. Originally developed to study Lie groups and Lie algebras, their use has extended into number theory, topology, and algebraic geometry, but they are also interesting in their own right. For us, they will provide a very concrete example of a category whose objects are not sets and how one can make progress in studying such a category. Only basic familiarity with groups and power series is assumed.