In this master thesis we will describe basic cosmological concepts and layout evidence for accelerated expansion of the universe. In introduction we will present facts and assumptions about universe in which we live based on different astronomical surveys. Composition of universe is described, and we introduced the assumption that universe is homogeneous and isotropic on big scales, and that Hubble’s law shows that recessional velocity of galaxies is proportional to its distance. We have used Doppler’s effect to express connections between redshift and distance and to write Hubble’s law in different form, showing proportionality between redshift and distance. In second chapter we have described models of the universe which originate from Friedmann equation based on Robertson-Walkers metrics and Einstein’s gravitational equation. Based on redshifts of different galaxies we have search for the model that best fits the observations. In third chapter we have used the measurements of redshifts and distances for Supernova type Ia and determined the acceleration factor of expansion of the universe. At the end, we have discussed topic of the expansion of the universe in a way that it is comprehensive for the pupils in high school.