In this thesis we study superbridge index of knots and examine
some of its properties and relations with other knot invariants.
Also we calculate superbridge index for some knots.
In Chapter 1 we introduce definitions, notions and terminology and
investigate some relations between superbridge index and other
knot invariants. In Chapter 2 we present two moves on knots which
do not increase the superbridge numbers. In Chapter 3 we examine
knots having odd superbridge index and show that there are only
finitely many knots with superbridge index 3. Moreover, we show
that the list $\{ 3_1 ,\ 4_1 ,\ 5_2 ,\ 6_1 ,\ 6_2 ,\ 6_3 ,\ 7_2 ,\
7_3 ,\ 7_4 , \ 8_4 ,\ 8_7,\ 8_9 \}$ contains all knots with
superbridge index 3. And we get a new upper bound for superbridge
index related with bridge index. In chapter 4 we consider the
connected sums of two knots and introduce some results about the
superbridge index for composite knots. Also we study marginal
knots and strongly marginal knots and propose some problems about
those knots. In Chapter 5 we supply the best known estimates of
the superbridge index for all prime knots up to nine crossings.