Topology, a field of mathematics concerned with the properties of space that are preserved under continuous transformations, has significant implications in various scientific domains. Knot theory, a branch of topology, examines the embeddings of circles in 3-dimensional space and plays a crucial role in understanding complex structures in molecular biology, statistical mechanics, and quantum field theory. This paper aims to delve into the nuances of knot theory through the lens of algebraic topology to uncover underlying patterns and relations. The study employs advanced algebraic tools such as homology and cohomology groups to analyze the fundamental properties of knots. Our findings reveal new insights into the classification of knots and their invariants, providing a deeper understanding of their algebraic structure. These results suggest potential applications in solving longstanding problems in topology and related fields. In conclusion, this research not only enhances the comprehension of knot theory but also sets the stage for further investigations into the interplay between topology and other mathematical disciplines.