Mathematics MA2224
Textbook
A textbook you could refer to (one that has more in it than we will cover) is The elements of integration and Lebesgue measure, by Robert G. Bartle, which is published by Wiley in the Wiley classics library [Hamilton 515.43 K62, S-LEN 515.43 K62, Ussher Stacks PL-311-680].
If you look at the Bartle book, you'll see he says you can do the end bits first or last, and I plan to simplify what he does to some extent, starting with the material at the end (chapter 11).