Many physical problems that are usually solved by differential equation methods can be solved more effectively by integral equation methods. Such problems abound in applied mathematics, theoretical mechanics, and mathematical physics. The second edition of this widely used book continues the emphasis on applications and presents a variety of techniques with extensive examples. Additional material has been added throughout the book. The chapters dealing with differential equations and singular integral equations have been considerably expanded. Thus, the book is ideal as a text for a beginning graduate level course. Its treatment of boundary value problems and an extended, and up-to-date bibliography will also make the book useful to research workers in many applied fields.