Galaxy formation is an enormously complex discipline due to the many physical processes that play a role in shaping galaxies. The objective of this thesis is to study galaxy formation with two different approaches: First, numerical simulations are used to study the structure of dark matter and how galaxies form stars throughout the history of the Universe, and secondly it is shown that observations of gamma-ray bursts (GRBs) can be used to probe galaxies with active star formation in the early Universe.

A conclusion from the hydrodynamical simulations is that the galaxies from the stateof-the-art cosmological simulation, Illustris, follow a tight relation between star formation rate and stellar mass. This relation agrees well with the observed relation at a redshift of z = 0 and z = 4, but at intermediate redshifts of z ' 2 the normalisation is lower than in real observations. This is highlighted as an important problem to solve in future cosmological simulations. Another important result from this thesis is that abundances of different chemical elements (e.g. Fe, S, and Ni) can be measured out to z ' 5 with GRB host observations. Pushing the observations of chemical abundances to higher redshift is important, since it helps constraining chemical evolution models at high redshift.

A new project studying how the population of galaxies hosting GRBs relate to other galaxy population is outlined in the conclusion of this thesis. The core of this project will be to quantify how the stellar mass function of GRB host galaxies is affected by the fact that GRBs appear mainly to happen in low-metallicity galaxies. Solving this problem will make it possible to derive the total cosmic star formation rate more reliably from number counts of GRBs.