Lecture 3: The density of squarefree values taken by a polynomial

It is well known that the density of integers that are squarefree is 6/π2, giving one of the more intriguing occurrences of π where one might not a priori expect it! A natural next problem that has played an important role in number theory is that of understanding the density of squarefree values taken by an integer polynomial. We survey a number of recent results on this problem for various types of polynomials some of which use the ABC Conjecture and some of which do not.