From the reviews:

"...The authors have succeeded admirably in their aims; the book is a real pleasure to read".
Mathematical Reviews, 1986

"This is a book of interest to any having to work with differential equations, either as a reference or as a book to learn from. The authors have taken trouble to make the treatment self-contained. It (is) suitable required reading for a PhD student. Although the material has been developed from lectures at Stanford, it has developed into an almost systematic coverage that is much longer than could be covered in a year's lectures".
Newsletter, New Zealand Mathematical Society, 1995

"Primarily addressed to graduate students, this elegant book is accessible and useful to a broad spectrum of applied mathematicians".
Revue Roumaine de Mathematiques Pures et Appliquees, 1985

• Introduction
• Linear Equations
  • Laplace's Equation
  • The Classical Maximum Principle
  • Poisson's Equation and the Newtonian Potential
  • Banach and Hilbert Spaces
  • Classical Solutions; the Schauder Approach
  • Sobolev Spaces
  • Generalized Solutions and Regularity
  • Strong Solutions
• Quasilinear Equations
  • Maximum and Comparison Principles
  • Topological Fixed Point Theorems and Their Application
  • Equations in Two Variables
  • Hölder Estimates for the Gradient
  • Boundary Gradient Estimates
  • Global and Interior Gradient Bounds
  • Equations of Mean Curvature Type
  • Fully Nonlinear Equations
• Bibliography
• Epilogue
• Subject Index
• Notation Index