This thesis material shows how to estimate the values between given data points using polynomial interpolation, a key technique used in many scientific fields. We focus on the theoretical and practical aspects of polynomial interpolation, specifically Lagrange and Newton forms which are quite commonly used methods. By examining how these methods solve interpolation problems and minimize errors, we learned which method works best under different conditions. The results show that choosing the right interpolation method is crucial for accuracy, depending on the data's nature and the function being approximated. Overall, this study enhances our understanding of interpolation methods and their practical applications in real-world scenarios.