We complete the basic equations of cosmology by introducing the second Friedmann and continuity equations. We next introduce the equation of state parameter, and describe the evolution of the universe in the simplest cosmological models: matter-only, radiation-only, and lambda-only. We introduce the concept of a cosmological horizon, and explain how to calculate the age of the universe in a given model. Along the way, we establish the fiducial cosmological model -- a set of cosmological parameters that we will use for all our results in the remainder of the book. We end by introducing two observationally accessible distance measures -- luminosity distance and angular-diameter distance.

This chapter introduces some of the basic tools of a cosmologist, including scale factor, redshift, and comoving distance. We start with the Hubble law, which is a key consequence of the expanding universe. Next, we cover the possible geometries of space (positively and negatively curved, and flat), and the associated Friedmann--Lemaître--Robertson--Walker metric that describes them. This leads us to define distance measures in cosmology, and introduce the Friedmann equation that describes the evolution of the universe given its contents. We end by discussing the role of critical density and curvature.