The classical de Rham and the Hodge Decomposition theorems deal with the singular cohomology of a projective manifold with coefficients in the non-zero complex numbers C*. Non abelian Hodge theory seeks to generalize this picture, with complex reductive groups, such as the general linear group, playing the role of the abelian C*. Instead of cohomology groups, we obtain complex algebraic varieties and their singular cohomology groups carry additional structures. The P=W Conjecture seeks to relate two of these non-classical structures. This talk is devoted to introducing the audience to this circle of ideas and related developments.