It has always been a temptation for mathematicians to present the
crystallized product of their thoughts as a deductive general theory and
to relegate the individual mathematical phenomenon into the role of an
example. The reader who submits to the dogmatic form will be easily
indoctrinated. Enlightenment, however, must come from an understanding
of motives; live mathematical development springs from specific natural
problems which can be easily understood, but whose solutions are
difficult and demand new methods of more general significance. The
present book deals with subjects of this category. It is written in a
style which, as the author hopes, expresses adequately the balance and
tension between the individuality of mathematical objects and the
generality of mathematical methods. The author has been interested in
Dirichlet's Principle and its various applications since his days as a
student under David Hilbert. Plans for writing a book on these topics
were revived when Jesse Douglas' work suggested to him a close
connection between Dirichlet's Principle and basic problems concerning
minimal sur- faces. But war work and other duties intervened; even now,
after much delay, the book appears in a much less polished and complete
form than the author would have liked.
