Proof - the biggest and most powerful notion in mathematics, yet nowadays it's not properly introduced and defined until you hit Uni-level maths, crazy huh? I bought this book after sitting a module at uni specifically on proof itself, and can heartily recommend this as a bridge into higher level mathematics.
This books has an engaging, conversational style making it perfect for self-study or extra-curricula reading - it very much gave me the feeling of being in a tutorial at points! There are lots of exercises to hit home the important ideas and methods, to get you using the skills that you've learned. A very helpful text.