• Nonrepresentational Sculpture
• Abstract Sculpture
• Nonobjective Sculpture
• Biomorphic Sculpture
• Formalist Sculpture
• Conceptual Sculpture
• Process Sculpture
• Minimal Sculpture
• Post-Minimal Sculpture
• Installation Sculpture

"there are two main kinds of Nonrepresentational sculpture.

Abstract sculpture uses nature not as subject matter to be represented but as a source of formal ideas. For sculptors who work in this way, the forms that are observed in nature serve as a starting point for a kind of creative play, the end products of which may bear little or no resemblance to their original source.

Nonobjective sculpture is a more completely nonrepresentational form that does not even have a starting point in nature.  It arises from a constructive manipulation of the sculptor's generalized, abstract ideas of spatial relations, volume, line, colour, texture, and so on.  The approach of the nonobjective sculptor has been likened to that of the composer of music, who manipulates the elements of his art in a similar manner."

- Britannica.com
  
"Biomorphic is a term most commonly associated with abstract art to describe a form that is irregular or organic, often derived from shapes found in nature.  Biomorphic forms are frequently found in Surrealist art, most notably in the paintings of Yves Tanguy and the sculpture of Arp and Henry Moore."

- The Thames & Hudson Dictionary of Art Terms
   
Formalism emphasizes the form or structural qualities of a work over its content or context.  Formalist sculpture's primary emphasis is in the relationships of shapes and the lines those shapes make.  This approach is in contrast to process and conceptual sculpture.  The objects and installations of process sculpture have an emphasis on how the artist gets the job done.  Conceptual sculpture's primary emphasis is the communication of the idea behind the work.  In conceptual sculpture the "concept is the most important aspect of the work...The idea becomes the machine that makes the art..."

- Sol LeWitt "Paragraphs on Conceptual Art", Artforum, summer, 1967
 
Minimal art is "an abstract style of painting and sculpture developed in New York in the 1960s.  In reaction to abstract expressionism, it aims to eliminate self-expression by using geometrical shapes and unmodulated colours."

- The Macmillan Encyclopedia 2001
  
"Minimalism's sense of detachment and reduction to pure, self-referential form is best seen in sculpture.  Of particular importance to Minimal sculpture, by such artists as Carl Andre, Dan Flavin, Donald Judd, and others, is its relation to the space in which it is located, asserting an inextricable bond between the object and its context.  Furthermore, that many sculptures were produced as series demonstrates Minimalism's propensity for subtle permutations of prescribed forms. Minimal objects (or their components) were not fabricated by the artists themselves but rather by other people working from plans drawn up by the artists."

- artweb.com
  
"By the mid-1960s, another orientation to sculpture emerged out of Minimalism in the work of such artists as Eva Hesse, Martin Puryear, and Richard Serra. Their art is a synthesis of Abstract Expressionist gesture and improvisation coupled with the literal nature of  Minimalism.   Sometimes named Post-Minimal, this work tends to be more sensual and organic than Minimal art exploiting the elasticity and tactility of unconventional materials." 

- artweb.com
 
"Installation art is art that uses sculptural materials and other media to modify the way we experience a particular space.  Installation art incorporates almost any media to create a visceral and/or conceptual experience in a particular environment. Materials used in contemporary installation art range from everyday and natural materials to new media such as video, sound, performance, computers and the internet." 

- wikipedia.org