Knots and crossings
Virtual knots and links
CURVES IN THE PLANE
VIRTUAL LINKS
ORIENTED VIRTUAL LINK DIAGRAMS
Linking invariants
CONDITIONAL STATEMENTS
WRITHE AND LINKING NUMBER
DIFFERENCE NUMBER
CROSSING WEIGHT NUMBERS
A multiverse of knots
FLAT AND FREE LINKS
WELDED, SINGULAR, AND PSEUDO KNOTS
NEW KNOT THEORIES
Crossing invariants
CROSSING NUMBERS
UNKNOTTING NUMBERS
UNKNOTTING SEQUENCE NUMBERS
Constructing knots
SYMMETRY
TANGLES, MUTATION, AND PERIODIC LINKS
PERIODIC LINKS AND SATELLITE KNOTS
Knot polynomials
The bracket polynomial
THE NORMALIZED KAUFFMAN BRACKET POLYNOMIAL
THE STATE SUM
THE IMAGE OF THE F-POLYNOMIAL
Surfaces
SURFACES
CONSTRUCTIONS OF VIRTUAL LINKS
GENUS OF A VIRTUAL LINK
Bracket polynomial II
STATES AND THE BOUNDARY PROPERTY
PROPER STATES
DIAGRAMS WITH ONE VIRTUAL CROSSING
The checkerboard framing
CHECKERBOARD FRAMINGS
CUT POINTS
EXTENDING THE KAUFFMAN-MURASUGI-THISTLETHWAITE THEOREM
Modifications of the bracket polynomial
THE FLAT BRACKET
THE ARROW POLYNOMIAL
VASSILIEV INVARIANTS
Algebraic structures
Quandles
TRICOLORING
QUANDLES
KNOT QUANDLES
Knots and quandles
A LITTLE LINEAR ALGEBRA AND THE TREFOIL
THE DETERMINANT OF A KNOT
THE ALEXANDER POLYNOMIAL
THE FUNDAMENTAL GROUP
Biquandles
THE BIQUANDLE STRUCTURE
THE GENERALIZED ALEXANDER POLYNOMIAL
Gauss diagrams
GAUSS WORDS AND DIAGRAMS
PARITY AND PARITY INVARIANTS
CROSSING WEIGHT NUMBER
Applications
QUANTUM COMPUTATION
TEXTILES
Appendix A: Tables
Appendix B: References by Chapter