The Whitney embedding theorem

Abstract: A fundamental theorem in differential geometry is proven in this essay. It is the embedding theorem due to Hassler Whitney, which shows that the ever so general and useful topological spaces called manifolds, can all be regarded as subspaces of some Euclidean space. The version of the proof given in this essay is very similar to the original from 1944. Modern definitions are used, however, and many illustrations have been made, wherever it helps the understanding.