In this talk, I intend to give a pedagogical, nonetheless biased, introduction to String Cosmology. After briefly reviewing the Lambda-CDM model and motivating inflation, we will remind ourselves that early universe cosmology remains singular and waiting for alternatives. That will be our cue to consider string theory to define our gravity sector and string thermodynamics to define our matter sector. We will learn how that doesn't work, unless we consider more string corrections (in fact, infinity of them!). Once we are stringy enough, we will be able to build a full cosmological model that is non-singular and already poses itself as an alternative to inflation at the background level.