This monograph i s an expanded versio n of a CBM S series of lectures deliv-
ered in Miami in January, 1984. A s in the lectures » our goa l is to provide a n
introduction t o minimax methods in critical point theory and their applicatio n
to problems in differential equations . Th e presentation of the abstract minima x
theory i s essentially self-contained . Mos t o f the application s ar e to semilinea r
elliptic partial differential equation s and a basic knowledge of linear elliptic the-
ory is required for this material. A n overview is given of the subject matte r in
Chapter 1 and a detailed study is carried out in the chapters that follow .
Many friend s hav e contributed t o my study an d Organizatio n o f this mate-
rial. I thank in particular Antonio Ambrosetti, Abbas Bahri, Vieri Benci, Henri
Berestycki, Hai m Brezis , Michae l Crandall , Edwar d Fadell , Suffia n Husseini ,
Jürgen Moser , an d Loui s Nirenberg fo r thei r inspiration , encouragement , an d
advice. Th e CBMS Conference was hosted by the Mathematics Departmen t of
the University of Miami. Further thanks are due to the members of the depart-
ment, especially t o Shair Ahmad an d Alan Lazer for thei r efficient handlin g of
the meeting and their kind hospitality.