Complete intersection dimension Luchezar L\. Avramov, Vesselin N\. Gasharov, and Irena V\. Peeva Preprint, 1995. \abstract A new homological invariant is introduced for a finite module over a commutativenoetherian ring: its CI-dimension. In the local case, sharp quantitative and structural data are obtained for modules of finite CI-dimension, providing the first class of modules of (possibly) infinite projective dimension with a rich structure theory of free resolutions. \endabstract