Summary: In these lectures we plan to present a survey of certain aspects of harmonic analysis on a Heisenberg nilmanifold \(\Gamma\backslash\mathbb H^n\). Using Weil-Brezin-Zak transform we obtain an explicit decomposition of \(L^2(\Gamma\backslash\mathbb H^n)\) into irreducible subspaces invariant under the right regular representation of the Heisenberg group. We then study the Segal-Bargmann transform associated to the Laplacian on a nilmanifold and characterise the image of \(L^2(\Gamma\backslash\mathbb H^n)\) in terms of twisted Bergman and Hermite Bergman spaces.