Network science, a multidisciplinary field, employs mathematical approaches to model and analyze complex systems as networks or graphs. This paper provides an overview of the fundamental concepts, mathematical modeling techniques, analysis methods, and applications of network science. It emphasizes the importance of mathematical approaches in understanding the structure and dynamics of networks in various domains, including social, biological, and technological networks. The paper also discusses challenges such as scalability and incorporating dynamics, along with future research directions. Overall, mathematical approaches are essential for advancing network science and unlocking new insights into complex systems.