Computing the Optical Properties of Large Systems This work addresses the computation of excited state properties of systems containing thousands of atoms. To achieve this the author combines the linear response formulation of time dependent density functional theory (TDDFT) with linear scaling techniques known from ground state density functional theory. This extends the range of TDDFT which on its own cannot tackle many of the large and interesting systems in materials science and computational biology. The strengths of the approach developed in this work are demonstrated on a number of problems involving large scale systems including exciton coupling in the Fenna Matthews Olson complex and the investigation of low lying excitations in doped p terphenyl organic crystals.