Upon its initial 1977 publication, this volume made recent accomplishments in its field available to advanced undergraduates and beginning graduate students of mathematics. Requiring only some familiarity with advanced calculus and rudimentary complex function theory, it covered discoveries of the previous three decades, a particularly fruitful era. Now it remains a permanent, much-cited contribution to the ever-expanding literature on partial differential equations. Author Martin Schechter chose subjects that will motivate students and introduce them to techniques with wide applicability to problems in partial differential equations as well as other branches of analysis. Uniform in theme and outlook, the text features problems that consider existence, uniqueness, estimates, and regularity of solutions. Topics include existence of solutions, regularity of constant and variable coefficients, the Cauchy problem, properties of solutions, boundary value problems in a half-space, the Dirichlet problem, general domains, and general boundary value problems.