This paper introduces the theory of knots, focusing on the construction of knot invariants such as the Jones polynomial and Vassiliev invariants, and their connections to other areas of mathematics, including Lie algebras. It begins with an overview of the development of knot theory, influenced by the discovery of the Jones polynomial in 1984 and the subsequent surge in research. The paper explores the relationship between knots and algebra, as well as their connections to physics, starting with the Jones polynomial and its bracket model. It then introduces Vassiliev invariants and the relationship between Lie algebras and knot theory. The key result in knot theory is Reidemeister's theorem, which states that two knot diagrams represent equivalent loops if and only if one can be transformed into the other using a finite sequence of Reidemeister moves. These moves are illustrated in Figure 1 and are local changes that modify the diagram only in specific areas. Move zero is particularly important but does not affect the diagram's essential relationships. The paper discusses invariants of knots and links, which are numbers or algebraic expressions that remain unchanged under Reidemeister moves. The linking number is an example of such an invariant, measuring how many times one curve winds around another. The linking number is invariant under Reidemeister moves, as shown by the fact that it is unaffected by the first move and the second move either creates or destroys two crossings of opposite sign. The third move also does not affect the linking number. The paper continues to explore these concepts, highlighting their significance in understanding the topology of knots and links.This paper introduces the theory of knots, focusing on the construction of knot invariants such as the Jones polynomial and Vassiliev invariants, and their connections to other areas of mathematics, including Lie algebras. It begins with an overview of the development of knot theory, influenced by the discovery of the Jones polynomial in 1984 and the subsequent surge in research. The paper explores the relationship between knots and algebra, as well as their connections to physics, starting with the Jones polynomial and its bracket model. It then introduces Vassiliev invariants and the relationship between Lie algebras and knot theory. The key result in knot theory is Reidemeister's theorem, which states that two knot diagrams represent equivalent loops if and only if one can be transformed into the other using a finite sequence of Reidemeister moves. These moves are illustrated in Figure 1 and are local changes that modify the diagram only in specific areas. Move zero is particularly important but does not affect the diagram's essential relationships. The paper discusses invariants of knots and links, which are numbers or algebraic expressions that remain unchanged under Reidemeister moves. The linking number is an example of such an invariant, measuring how many times one curve winds around another. The linking number is invariant under Reidemeister moves, as shown by the fact that it is unaffected by the first move and the second move either creates or destroys two crossings of opposite sign. The third move also does not affect the linking number. The paper continues to explore these concepts, highlighting their significance in understanding the topology of knots and links.