LOOP APPROACHES TO GAUGE FIELD-THEORIES

Basic mathematical and physical concepts in loop- and path-dependent f ormulations of Yang-Mills theory are reviewed and set into corresponde nce. We point out some problems peculiar to these non-local approaches , in particular those associated with defining structure on various ki nds of loop spaces. The issues of classical loop equations, differenti al operators, lattice gauge theory, loop algebras, and canonical quant ization are discussed in some detail, and the paper concludes with an extensive list of references.