Approximation theory is a field of mathematics that focuses on finding simpler functions that can approximate complex functions. It plays a crucial role in various applications where it may be challenging to analyze functions directly.The study of approximation theory explores into the theoretical foundations of approximation algorithms and investigates their convergence properties. By understanding these theoretical aspects, researchers can develop efficient algorithms and numerical methods to solve practical problems. This interdisciplinary field involves a combination of mathematical analysis, functional analysis, numerical analysis, and computational mathematics.This book will help mathematicians, researchers, graduate students, and professionals working in areas such as applied mathematics, numerical analysis, computational mathematics, mathematical modeling, and data analysis. It provides valuable insights into the theoretical foundations of approximation theory and its practical applications. Readers with a strong background in mathematics and a keen interest in approximation theory will find this book particularly beneficial. It serves as a comprehensive reference for those seeking a deeper understanding of the field and as a guide for applying approximation techniques in various domains.