The theory of Hardy spaces has close connections to many branches of mathematics including Fourier analysis, harmonic analysis, singular integrals, potential theory and operator theory, and has found essential applications in robust control engineering. For each application, the ability to represent elements of these classes by series or integral formulas is of utmost importance. This self-contained text provides an introduction to a wide range of representation theorems and provides a complete description of the representation theorems with direct proofs for both classes of Hardy spaces: Hardy spaces of the open unit disc and Hardy spaces of the upper half plane. With over 300 exercises, many with accompanying hints, this book is ideal for those studying Advanced Complex Analysis, Function Theory or Theory of Hardy Spaces. Advanced undergraduate and graduate students will find the book easy to follow, with a logical progression from basic theory to advanced research.

"Mathematicians working on related topics should find it a useful reference for statements and proofs of many of the classical results related the the Hardy spaces. Anyone teaching a course that includes Hardy spaces would find it a good source for homework problems."
Peter Rosenthal, CMS Notes

"... self-contained and clearly written text... The main strength of this book is a large number of exercises (over 300), which makes it a good textbook choice."
Marcin M. Bownik, Mathematical Reviews