Measuring flux ratios of high energy neutrinos is an alternative method to determine the neutrino mixing angles and the CP phase. We conduct a systematic analysis of the neutrino mixing probabilities and of various flux ratios measurable at neutrino telescopes. The considered cases are neutrinos from pion, neutron and muon-damped sources. The flux ratios involve measurements with and without taking advantage of the Glashow resonance. Explicit formulae in case of µ-τ symmetry (θ 13 = 0 and θ 23 = π/4) and its special case tri-bimaximal mixing (sin 2 θ 12 = 1/3) are obtained, and the leading corrections due to non-zero θ 13 and non-maximal θ 23 are given. The first order correction is universal as it appears in basically all ratios. We study in detail its dependence on θ 13 , θ 23 and the CP phase δ, finding that the dependence on θ 23 is strongest. The flavor compositions for the considered neutrino sources are evaluated in terms of this correction. A measurement of a flux ratio is a clean measurement of the universal correction (and therefore of θ 13 , θ 23 and δ) if the zeroth order ratio does not depend on θ 12 . This favors pion sources over the other cases, which in turn are good candidates to probe θ 12 . The only situations in which the universal correction does not appear are certain ratios in case of a neutron and muondamped source, which depend mainly on θ 12 and receive only quadratic corrections from the other parameters. We further show that there are only two independent neutrino mixing probabilities, give the allowed ranges of the considered flux ratios and of all probabilities, and show that none of the latter can be zero or one. Finally, we analyze situations in which θ 13 is sizable and θ 23 is close to π/4, and in which θ 13 is close to zero and θ 23 − π/4 is sizable. * email: werner.rodejohann@mpi-hd.mpg.de 1 Note that cosmic rays have already turned out to be very useful for neutrino physics because the zenith angle dependent deficit of muon neutrinos, which are created by cosmic rays in the Earth's atmosphere, has provided the first compelling evidence for neutrino oscillations.2 θ 23 is universal, i.e., the same for all probabilities. It depends in a characteristic way on the parameters, which we study in detail. The dependence on θ 23 is strongest. Since θ 12 is non-maximal and non-zero, no probability is zero or one, therefore high energy neutrinos are guaranteed to change their flavor. As neutrino flux ratios are functions of the mixing probabilities, they are most of the times given by a zeroth order expression and a first order correction. This allows for a comparably simple analytical understanding of the measurements in terms of their implications on the neutrino mixing parameters. If the zeroth order expression of a flux ratio is independent of θ 12 , then measuring the ratio means measuring the correction ∆ without any uncertainty due to our imprecise knowledge of θ 12 . Hence, the ratio is a good probe for U e3 , θ 23 − π/4 and δ. This happens typically for neutrinos from pion sour...