Many physical problems are most naturally described by systems of differential and algebraic equations. This book describes some of the places where differential-algebraic equations (DAEs) occur. The basic mathematical theory for these equations is developed and numerical methods are presented and analyzed. Examples drawn from a variety of applications are used to motivate and illustrate the concepts and techniques. The book develops guidelines for choosing different numerical methods, and discusses DAE codes, including the popular DASSL code. A discussion of backward differentiation formulas details why they have emerged as the most popular and best understood class of linear multistep methods for general DAEs. New to this edition is a chapter that brings the discussion of DAE software up to date.