Deep-inelastic electron-proton scattering (DIS) with initial state photon radiation is investigated using the H1 detector at HERA. The proton structure function F_2(x,Q^2) is measured for Bjorken-x values of 2 * 10^-5 < x < 2 * 10^-2 over a Q^2 range extending from 20 GeV^2, where perturbative QCD calculations are clearly valid, down to 0.35 GeV^2, where the influence of non-perturbative effects is large and only phenomenological models can describe the data.