In this chapter, the two main ingredients of the contemporary cosmological paradigm, or the new standard cosmology, are initially presented as a thought experiment that brings us back to the initial singularity from which the physical universe sprang. The thought experiment follows the trajectory of the contraction of matter and radiation, darkening galaxies, and ever hotter universe to the first hundreds of seconds when a violent inflation of the universe took place that we can understand speculatively and perhaps observe indirectly through the structure of gravitational waves. After 300,000 years of expansion of the universe, very energetic photons disrupted positively charged nuclei and negatively charged electrons in forming atoms. At that point, the atoms were formed, and photons scattered off, traveling through space and slowly losing energy due to expansion of the universe. The structures (stars and galaxies) started forming. The accelerated, rather than uniform, expansion of the universe and dark energy driving it were postulated in 1998. This feature is not as established as the Hot Big Bang model, but observational evidence is accumulating. The chapter provides a box with the basic physical elements of the new standard cosmological model.