A Moufang set is essentially a doubly transitive permutation group such that the point stabilizer contains a normal subgroup which is regular on the remaining points. These regular normal subgroups are called the root groups and they are assumed to be conjugate and to generate the whole group. Moufang sets play an significant role in the theory of buildings, they provide a tool to study linear algebraic groups of relative rank one, and they have (surprising) connections with other algebraic structures. In these course notes we try to present the current approach to Moufang sets. We include examples, connections with related areas of mathematics and some proofs where we think it is instructive and within the scope of these notes.