In this thesis two topics are discussed. The covariant formulation ofMaxwell’s equations of electromagnetism and the formulation of said equations in the context of a rotating frame of reference. Through the development of the necessary theories of Differential Geometry and Special Relativity we show how to formulateMaxwell’s equations in terms of the covariant derivative and in terms of the hodge operator and differential operator. Using this formulation we study the transformation properties of these equations under Lorentz transformations and we conclude that they remain invariant under said transformations. Secondly,we discuss literature concerning the problem of electromagnetism in the context of a rotating frame of reference. We show that the method of direct transformation to a rotating frame results in an unobservable frame of reference and we show that it is impossible to reconstruct Coriolis like forces in an observable frame of reference.