This introductory volume provides the basics of surface-knots and related topics not only for
researchers in these areas but also for graduate students and researchers who are not familiar
with the field.Knot theory is one of the most active research fields in modern mathematics.
Knots and links are closed curves (one-dimensional manifolds) in Euclidean 3-space and they
are related to braids and 3-manifolds. These notions are generalized into higher dimensions.
Surface-knots or surface-links are closed surfaces (two-dimensional manifolds) in Euclidean
4-space which are related to two-dimensional braids and 4-manifolds. Surface-knot theory
treats not only closed surfaces but also surfaces with boundaries in 4-manifolds. For example
knot concordance and knot cobordism which are also important objects in knot theory are
surfaces in the product space of the 3-sphere and the interval.Included in this book are basics
of surface-knots and the related topics of classical knots themotion picture method surface
diagrams handle surgeries ribbon surface-knots spinning construction knot concordance and
4-genus quandles and their homology theory and two-dimensional braids.
