Abstract
We introduce the category of almost alternating links: nonalternating links which have a projection for which one crossing change yields an alternating projection. We extend this category to m-almost alternating links which require m crossing changes to yield an alternating projection. We show that all but five of the nonalternating knots up through eleven crossings and links up through ten crossing are almost alternating. We also prove that a prime almost alternating knot is either a hyperbolic knot or a torus knot. We then obtain a bound on the span of the bracket polynomial for m-almost alternating links and discuss applications.
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