In the following we survey the main results in the theory of measure and integration. The main references I have used are [EG], [S] and [R], in that order. Proofs are usually only sketched, but I have attempted to provide a reasonable amount of motivation of both proofs and results. We will often consider general measures $\mu$ on an arbitrary set $X$. But you should first think of the most important case - Lebesgue measure in $\IR^n$. To fix ideas, take $n = 2$.