You don’t need to read any of these for the purposes MATH0005, but if you want to learn more about the topics covered here are my recommendations.
The third year course MATH0037 Logic contains some material on set theory. If you want to learn about formal (ZFC) set theory and can’t wait for MATH0037, Classic Set Theory by Derek Goldrei is a great introduction. It was written as an Open University textbook so is designed for self-study. Naive Set Theory by Paul Halmos gives an idea of what formal set theory is all about without getting into all of the axiomatic details.
The problems with unrestricted set comprehension mentioned briefly in the text are explained nicely in the Stanford Encyclopedia of Philosophy entry for Russell’s Paradox, but you can find hundreds of other examples with an internet search. This short pdf by the philosopher Richard Pettigrew gives a short sketch of what goes wrong and how it is fixed formally.
Most basic algebra textbooks go into more detail on permutations than we do in 0005. I like A Concise Introduction to Pure Mathematics by Martin Liebeck a lot, and it has a nice application of the sign of a permutation to (not) solving the 15 puzzle. Topics in Algebra by I. Herstein is not always the easiest text but contains loads of interesting material if algebra is your thing, some of which is covered in MATH0006 Algebra 2. C. Pinter’s Book of Abstract Algebra is published by Dover so is cheap even if you want a hard copy, and covers permutations in chapters 7 and 8. It’s especially worthwhile if you want to learn more abstract algebra.