The new edition of Function of Several Variables is an extensive revision. Like the first edition it presents a thorough introduction to differential and integral calculus, including the integration of differential forms on manifolds. A new chapter on elementary topology makes the book more complete as an advanced calculus text; sections have been added introducing physical applications in thermodynamics, fluid dynamics, and classical rigid body mechanics. Many mathematicians were first introduced to basic analysis by the first edition. The second edition makes this material available, in improved form, to a new generation of students.