Many mathematical problems can be boiled down to the act of classifying objects up to some equivalence relation. One of the main tools that is used are so called moduli spaces; geometric spaces whose points are isomorphism classes of given objects. To this end, we are able to study abstract classification problems using familiar geometric methods. Like any quotient however, we lose some information, noticeably the data of the automorphism group attached to our points. Hence, to get a full picture of our problem, we need some way to encode automorphisms on our geometric space. This problem is solved by moduli stacks which I will introduce in this talk via the familiar language of differential geometry. Only the first quarter of the Geometry core class will be requisite knowledge as well as a healthy propensity to disregard technical details.