The future gamma-ray experiment CTA plans to measure the fluxes of blazars in the energy range from 30 GeV to 100 TeV with sensitivity 10 times superior to present measurements. Intergalactic magnetic fields can be measured through observations of the secondary photons through time delay in blazar flairs, signatures in spectra and extended emission around the point sources. Same data can be used to study the imprints of the hypothetical axion-like particles, one of main Dark Matter candidates, in the spectra of gamma-ray sources.

The goal of this thesis is to model the above phenomena, taking into account the recent models of extragalactic background light and make model predictions for the future CTA measurements.

During first year it is planed to study the uncertainty in existing extragalactic background light models to estimate it's contribution to the existing anomaly in transparency of the Universe in TeV energies.

The second year is devoted to systematic study of intergalactic magnetic field effects in the gamma-ray measurements with one of existing public three-dimensional cascade codes, taking into account the results of the first year study of the extragalactic background light.

The third year will be devoted to the study of possible imprints of axion-like particles to gamma-ray spectra built upon the models developed during the first and the second years.