Our Universe is filled with a mind-blowing diversity and different types and appearances of galaxies. Finding out about how they formed and evolved is one of the most challenging tasks in astronomy. When looking about 10 billion years back, to an epoch about 3 billion years after the big bang, we can see galaxies at earlier stages of their lives. In this talk, studies of different kinds of galaxies in the early universe will be presented. Two examples of the very intriguing population of massive quiescent z~2 galaxies were analyzed in terms of their stellar populations and morphologies. As the spectroscopic sample is still small, especially for galaxies at the faint end of the luminosity function, we make use of the biggest available "telescopes" in the universe: We search for red z~2 galaxies whose apparent brightnesses have been boosted by the Gravitational Lensing effect of intermediate redshift galaxy clusters with available mass models. Our findings indicate older ages for these galaxies than expected. Also, their remarkable compactness was corroborated. Furthermore, I'm going to present a study of a special case of so-called Damped Lyman-alpha Absorbers (DLAs), with two intervening galaxies in the line of sight of a higher-redshift QSO, which is also one example of only about a dozen known galaxy counterparts of a DLA. It fits into the emerging paradigm that galaxies which are responsible for higher metallicity DLAs are more massive and luminous than typical DLA galaxies. Motivated by that particular discovery, during the past few years we have undertaken a survey targeting candidate dust-reddened quasars missing in the sample from Sloan Digital Sky Survey. Spectroscopic follow-up with the NOT and the NTT has demonstrated a very high success rate of our selection (>90%). The main motivation is to search for quasars reddened by foreground dusty galaxies and we have found several such examples. We have also serendipitously found quasars with abnormal, very UV-steep extinction curves as well as a large number of broad absorption line quasars (BALs). The latter allow us to study the dependence of the BAL QSO population on redshift, reddening and luminosity. The results show a strong evolution of the BAL QSO fraction with cosmic time, with a peak at z~2.5 where several quantities in the Universe are also found to peak or vary. In addition,the dependence of this fraction with reddening and luminosity provides new constraints on the models for broad absorption origin in quasars. We are currently carrying out a pilot study of a search for even redder quasars selected from a combination of SDSS, UKIDSS and WISE photometry with the aim of selecting very dust-obscurred quasars or high-redshift BALs at z>2. Preliminary results from the first run et the NOT in March 2015 of the brightest candidates show very promising results which will also be briefly shown in the talk.