This second edition integrates the newly developed methods with classical techniques to give both modern and powerful approaches for solving integral equations. It provides a comprehensive treatment of linear and nonlinear Fredholm and Volterra integral equations of the first and second kinds. The materials are presented in an accessible and straightforward manner to readers, particularly those from non-mathematics backgrounds. Numerous well-explained applications and examples as well as practical exercises are presented to guide readers through the text. Selected applications from mathematics, science and engineering are investigated by using the newly developed methods. This volume consists of nine chapters, pedagogically organized, with six chapters devoted to linear integral equations, two chapters on nonlinear integral equations, and the last chapter on applications. It is intended for scholars and researchers, and can be used for advanced undergraduate and graduate students in applied mathematics, science and engineering. Key Features: ○ Treatment of integral equations without having extensive background in mathematics for non-mathematics students ○ A concise introduction to highlight the classifications of integral equations and calculus material ○ Presents up-to-date developments and approaches in the field of integral equations ○ Includes more theorems, new techniques, well-explained new examples and scientific applications ○ Includes adomian decomposition method and the variational iteration method to provide insight-oriented approaches ○ Includes two exclusive chapters to handle the nonlinear Volterra and Fredholm integral equations ○ Detailed sections on using the regularization method to solve the Fredholm integral equations of the first kind and usage of weakly-singular linear and nonlinear integral equations

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