In this note I present some aspects of the mathematical theory of epidemics, with particular attention to the case of a new emerging infection, as in the case of COVID-19. I start with the definition of basic reproduction number $R_0$, and present its relationship with the exponential growth rate at the beginning of an epidemic and with potential for control in simple deterministic models. I then discuss the corresponding stochastic models, showing that in this case the probability that the introduction of a few infected individduals results into an epidemic outbreak depends on the value of $R_0$. Finally, I will mention the structure of complex models that are currently used as support for the actions of the health authorities.