Algebraic structures for classical knots, singular knots and virtual knots

The purpose of this thesis is to establish algebraic structures on knots. Knot theory is a field in mathematics that investigates the properties and structures of knots. The main objective is to define knot invariants for the purpose of classifying knots. In order to do this, the thesis first provides some fundamental definitions of knots and links. Then we define the colorability of the knot, which we can use as a knot invariant. To further elaborate on this subject, we give definitions of the algebraic structures known as quandle, singquandle, and bondle. Using these determined structures, we provided variables for classifying the circuit topology. Circuit topology refers to a mathematical method used to classify the categorizes of connections between contacts. This thesis aims to classify the structure of proteins using circuit topology and knot theory. Consequently, we define an invariant for the circuit topology. At the end, the thesis determines these structures on virtual knots. In addition, it offers a definition and an example instance of this topic.