The abstract concepts of metric spaces are often perceived as difficult. This book offers a unique approach to the subject which gives readers the advantage of a new perspective on ideas familiar from the analysis of a real line. Rather than passing quickly from the definition of a metric to the more abstract concepts of convergence and continuity, the author takes the concrete notion of distance as far as possible, illustrating the text with examples and naturally arising questions. Attention to detail at this stage is designed to prepare the reader to understand the more abstract ideas with relative ease.

While there are many books on functional analysis, Elements of Abstract Analysis takes a very different approach. Unlike other books, it provides a comprehensive overview of the elementary concepts of analysis while preparing students to cross the threshold of functional analysis.The book is written specifically for final-year undergraduate students who should already be familiar with most of the mathematical structures discussed - for example, rings, linear spaces, and metric spaces - and with many of the principal analytical concepts - convergence, connectedness, continuity, compactness and completeness. It reviews the concepts at a slightly greater level of abstraction and enables students to understand their place within the broad framework of set-based mathematics.Carefully crafted, clearly written and precise, and with numerous exercises and examples, Elements of Abstract Analysis is a rigorous, self-contained introduction to functional analysis that will also serve as a text on abstract mathematics.