Aimed primarily at undergraduate level university students, An Illustrative Introduction to Modern Analysis provides an accessible and lucid contemporary account of the fundamental principles of Mathematical Analysis. With 99 graphic illustrations which complement the rigorous mathematical reasoning, this book allows the reader to develop a strong geometric intuition. Containing far beyond just theorems and rpoofs, it offers comments on the "know-how" and motivations for "why we do what we do". The themes treated include Metric Spaces, General Topology, Continuity, Completeness, Compactness, Measure Theory, Integration, Lebesgue Spaces, Hilbert Spaces, Banach Spaces, Linear Operators, Weak and Weak* Topologies. Suitable both for classroom use and independent reading, this book is ideal preparation for further study in research areas where a broad mathematical toolbox is required, such as in Partial Differential Equations, Calculus of Variations, Harmonic Analysis, Functional Analysis, Geometric Analysis, Numerical Analysis and Applied Mathematics