On hyperbolic 3-orbifolds of small volume

This thesis is concerned with hyperbolic 3-orbifolds of small volume. An n-orbifold is a space which locally, i.e. in a neighborhood of any point, looks like a quotient of Euclidean space \(\mb{R}^n\). We are interested in those spaces which may be equipped with hyperbolic geometry, i.e. are locally modeled on the quotient \(\mb{H}^n\) by a discrete subgroup of its isometries. Following the work of Meyerhoff and Adams we classify minimal volume orbifolds with one rigid and one nonrigid cusp. We then discuss joint work with J. DeBlois, A. H. Ekanayake, M. Fincher, A. Gharagozlou, and P. Mondal on establishing a census of orbifolds commensurable with the figure eight knot complement