This thesis provides a partial classification of all 3-stranded pretzel knots K=P(p,q,r) with unknotting number one. Scharlemann-Thompson, and independently Kobayashi, have completely classified those knots with unknotting number one when p, q, and r are all odd. In the case where p=2m, we use the signature obstruction to greatly limit the number of 3-stranded pretzel knots which may have unknotting number one. In Chapter 3 we use Greene's strengthening of Donaldson's Diagonalization theorem to determine precisely which pretzel knots of the form P(2m,k,-k-2) have unknotting number one, where m is an integer, m>0, and k>0, k odd. In Chapter 4 we use Donaldson's Diagonalization theorem as well as an unknotting obstruction due to Ozsv\'ath and Szab\'o to partially classify which pretzel knots P(2,k,-k) have unknotting number one, where k>0, odd. The Ozsv\'ath-Szab\'o obstruction is a consequence of Heegaard Floer homology. Finally in Chapter 5 we explain why the techniques used in this paper cannot be used on the remaining cases. / text

This thesis is largely expository, and we provide a survey on unknotting operations. We examine these local transformations for classical, virtual and welded knots and use their properties to calculate upper bounds on unknotting numbers. In addition, the thesis contains some original work, such as the definition and properties of the algebraic unknotting numbers of virtual and welded knots, an algebraic reformulation of t4-conjecture, and a new method to tell if a knot can be turned into a torus knot with one crossing change. / Thesis / Master of Science (MSc)