This paper provides an introduction to knot theory, focusing on the construction of invariants such as the Jones polynomials and Vassiliev invariants, and their connections to other mathematical fields like Lie algebras. The essay begins with an overview of the development of knot theory influenced by the discovery of the Jones polynomial in 1984. It highlights the relationship between knots and algebra and physics, particularly through the Jones polynomial and the bracket model. The Reidemeister moves, which are fundamental to the combinatorial theory of knots, are introduced, along with the concept of invariants that remain unchanged under these moves. The linking number is presented as a simple example of an invariant, demonstrating how it can be calculated and remains consistent even when the diagram representing the curves is modified by Reidemeister moves.This paper provides an introduction to knot theory, focusing on the construction of invariants such as the Jones polynomials and Vassiliev invariants, and their connections to other mathematical fields like Lie algebras. The essay begins with an overview of the development of knot theory influenced by the discovery of the Jones polynomial in 1984. It highlights the relationship between knots and algebra and physics, particularly through the Jones polynomial and the bracket model. The Reidemeister moves, which are fundamental to the combinatorial theory of knots, are introduced, along with the concept of invariants that remain unchanged under these moves. The linking number is presented as a simple example of an invariant, demonstrating how it can be calculated and remains consistent even when the diagram representing the curves is modified by Reidemeister moves.