Polynomials play an important role in developing numerical and analytical methods to solve various practical problems of physics, mathematics, engineering and industry. This research and reference text reports and reviews recent developments and applications of different polynomials in numerical and analytical/semi-analytical methods for solving a variety of science and engineering problems. It contains contributions from leading experts in areas such as basic theory and concepts of polynomials, mathematical modelling, mathematical physics, engineering, high-order numerical methods for differential, integral and integro-differential equations, artificial intelligence, fuzzy and interval based models and beyond. This book would be useful for graduates and researchers of various sciences and engineering fields.