Title: Algebraic Structures for Knot Coloring Author: Martina Vaváčková Department: Department of Algebra Supervisor: doc. RNDr. David Stanovský, Ph.D., Department of Algebra Abstract: This thesis is devoted to the study of the algebraic structures providing coloring invariants for knots and links. The main focus is on the relationship between these invariants. First of all, we characterize the binary algebras for arc and semiarc coloring. We give an example that the quandle coloring invariant is strictly stronger than the involutory quandle coloring invariant, and we show the connection between the two definitions of a biquandle, arising from different approaches to semiarc coloring. We use the relationship between links and braids to conclude that quandles and biquandles yield the same coloring invariants. Keywords: knot, coloring invariant, quandle, biquandle iii