Chapter 6 of *The Foundations of Mathematics* by Ian Stewart and David Tall
covers a lot of this material at a similar level. The book
*Propositional and
Predicate Calculus: A Model of Argument* by Derek Goldrei goes far beyond what
we cover in MATH0005, but I recommend it if you want to know about logic in much
more depth. You can also take the 3rd year course
MATH0037
Logic.

Chapter 3
of the free online book *Discrete Mathematics: An Open
Introduction* by Oscar Levin
has material on propositional calculus and first order logic, though
it doesn’t use the same framework of well-formed formulas that we do and
the vocabulary they use is slightly different.