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.

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.

chapter 1|17 pages

Sets, mappings, countability and choice

chapter 2|46 pages

Metric spaces and normed spaces

chapter 3|26 pages

Completeness and applications

chapter 4|27 pages

Topological spaces and continuity

chapter 5|32 pages

Compactness and sequential compactness

chapter 7|34 pages

Measure theory on general spaces

chapter 8|42 pages

The Lebesgue integration theory

chapter 9|37 pages

The class of Lebesgue functional spaces

chapter 10|32 pages

Inner Product Spaces and Hilbert Spaces

chapter 11|45 pages

Linear operators on normed spaces

chapter 12|24 pages

Weak topologies on Banach Spaces

chapter 13|25 pages

Weak* topologies and compactness

chapter 14|19 pages

Functional properties of the Lebesgue spaces

chapter 15|84 pages

Solutions to the exercises