It is a common belief that topologically non-trivial configurations are so-lutions of equations of motion only of non-linear field theories. In this talk I will disprove this lore and show that free Maxwell’s theory admits such topo-logically non-trivial solutions. I will present a novel method of generating such solutions by applying conformal transformations with complex param-eters on known solutions expressed in terms of Bateman’s variables ( which I will describe). This has enabled us to get a wide class of solutions from ba-sic configuration like constant electromagnetic fields and plane-waves. I will present a covariant formulation of the Bateman’s construction and discuss the conserved charges associated with the conformal group as well as a set of four new types of conserved helicities. I will also present a formulation in terms of quaternions. This leads to a simple map between the electromag-netic knotted and linked solutions and flat connections of non-abelian SU(2) gauge theory. I will present the computation of the corresponding Chern-Simons charge in a class of solutions and it show that it takes integer values. I will briefly discuss the important issue of how to realize such topologically non-trivial electric and magnetic field in the laboratory