In this talk, I will introduce a useful way to record more information than ordinary coefficients for (co)homology by using the local coefficient system. I will first motivate this topic by comparing homology of orientable and non orientable manifolds. Next, I will define the local coefficient system and the homology using it. After that, I will introduce an equivalent way to define homology with local coefficients that is more algebraic and easier to compute. Finally, I will present an application of homology of local coefficients by generalizing the Poincare duality to non orientable manifolds.