Designed to bridge the gap between graduate-level texts in partial differential equations and the current literature in research journals, this text introduces students to a wide variety of more modern methods - especially the use of functional analysis - which has characterized much of the recent development of PDEs. *Covers the modern, functional analytic methods in use today -- especially as they pertain to nonlinear equations. *Maintains mathematical rigor and generality whenever possible -- but not at the expense of clarity or concreteness. *Offers a rapid pace -- with some proofs and applications relegated to exercises. *Unlike other texts -- which start with the treatment of second-order equations -- begins with the method of characteristics and first-order equations, with an emphasis in its constructive aspects. *Introduces the methods by emphasizing important applications. *Illustrates topics with many figures. *Contains nearly 400 exercises, most with hints or solutions. *Provides chapter summaries. *Lists references for further reading.