The fractional quantum Hall effect, a striking phenomenon from condensed matter physics, gives rise to a family of remarkable polynomials encoding its ground states on a sphere. These fractional quantum Hall (FQH) polynomials reveal rich algebraic and geometric structures, and their study connects naturally to areas of mathematics such as complex geometry, graph theory, and invariant theory. This three-part lecture series will introduce FQH polynomials from a mathematical perspective, assuming no physics background. In the first session, I will give a geometric introduction to these polynomials from first principles. The second session will reinterpret them in terms of regular graphs, highlighting their symmetries. The third session will connect FQH polynomials to the classical theory of invariants of binary forms and discuss recent ideas aimed at extending their machinery to higher genus Riemann surfaces. The talks are designed for a broad audience with some background in differential or Riemannian geometry. My goal is to make the beauty and depth of FQH polynomials accessible, and to show how ideas originating in physics can open new directions in pure mathematics.