Results of applications in contemporary mathematics are presented and the relevance of functional analysis to other areas is shown in this introduction for advanced undergraduate students.
It’s been a long journey, but after dipping into the book for years, I think I’ve finally had the stamina to learn all the proofs and finish it off. It’s very rewarding to take a break from focussing on lectures and get and understanding and overview of the subject instead. Bollobás is very clear, thorough, and I don’t think there are any mistakes (beyond the usual deliberate details lost in conciseness). The exercises also are good. One of the half dozen best books to read to get the full flavour of undergrad maths.