Minimal submanifolds: Encyclopedia of Mathematical Physics
  We give a quick tour through many of the classical results in the field of minimal submanifolds, starting at the definition. The field of minimal submanifolds remains extremely active and has very recently seen major developments that have solved many longstanding open problems and conjectures; for more on this, see the expanded version of this survey as well as recent surveys of Meeks and Perez, Perez, and Rosenberg. 
Tobias H. Colding and William P. Minicozzi II