This thesis will take a look at a branch of topology called knot theory. We will first look at what started the study of this field, classical knot theory. Knot invariants such as the Bracket polynomial and the Jones polynomial will be introduced and studied. We will then explore racks and biracks along with the axioms obtained from the Reidemeister moves. We will then move on to generalize classical knot theory to what is now known as virtual knot theory which was first introduced by Louis Kauffman. Finally, we take a look at a newer aspect of knot theory, twisted virtual knot theory and we defined new link invariants for twisted virtual biracks.