Author: Walter Rudin
This advanced textbook is aimed at students of mathematics, science, computer science and engineering at the junior, senior or graduate level who are studying analysis. It brings together the traditionally separate subjects of real analysis (including measure theory, integration, LpL^pLp-spaces, Hilbert and Banach spaces) and complex analysis (holomorphic functions, analytic continuation, HpH^pHp-spaces) into a single unified volume. The third edition adds a new chapter on differentiation and offers streamlined explanations in several sections. The writing is famously rigorous, with concise but complete proofs and challenging end‑of‑chapter exercises that build in difficulty as you go. It stands out for emphasising the intimate connections between different branches of analysis rather than treating them in isolation. Although demanding, it is often regarded as a classic reference in the field, and is well suited for a serious study of analysis—less so as a casual first introduction. The book is part of the “Student Series in Advanced Mathematics” and is published by McGraw‑Hill.