Type IIA topoisomerases are essential, universally conserved proteins that modify DNA topology by passing one segment of duplex DNA (the transfer, or T-segment) through a transient double strand break in a second segment of DNA (the gate, or G-segment) in an ATP-dependent reaction. Type IIA topoisomerases decatenate, unknot, and relax supercoiling in DNA to levels below equilibrium, resulting in global topology simplification. The mechanism underlying non-equilibrium topology simplification remains speculative, though several plausible models have been proposed. This thesis tests two of these, the bend angle and kinetic proofreading models, using single-molecule techniques. The bend angle model postulates that non-equilibrium topology simplification scales with the bend angle imposed on the G-segment DNA by a type IIA topoisomerase. To test this model, we used atomic force microscopy and single molecule Förster resonance energy transfer to measure the extent of bending imposed on DNA by three type IIA topoisomerases that span the range of topology simplification activity. We found that all proteins bent DNA, but the imposed bends are similar and cannot account for the differences among the enzymes. These data do not support the bend angle model and suggest that DNA bending is not the sole determinant of non-equilibrium topology simplification. Based on the assumption that the rates of collision between DNA segments is higher in knotted, linked, and supercoiled DNA than in topologically free or relaxed DNA, the kinetic proofreading model proposes that two successive binding events between a G-segment bound topoisomerase and a putative T-segment are required to initiate strand passage. As a result of the two step process, the overall rate of strand passage should scale with the square of the collision probability of two DNA segments. To test this model, we used magnetic tweezers to manipulate a paramagnetic bead tethered to the surface by two DNA molecules. By rotating the bead, we varied the proximity, and thus collision rate, of the two molecules to determine the relationship between collision probability and rate of strand passage. Our data indicate that the strand passage rate scales linearly with the collision probability, which is inconsistent with the kinetic proofreading model.