Hindman's theorem is a Ramsey-theoretic result asserting that, whenever one colours the set of natural numbers with finitely many colours, there will be an infinite set such that all numbers that can be obtained by adding finitely many elements from the set (no repetitions allowed) have the same colour. I will explore generalizations and extensions of this theorem: replacing "natural numbers" with "abelian group" and varying the number of colours, as well as the size of the desired monochromatic set, yields a plethora of very interesting results.