This book aims to handle different application problems of science and engineering using expert Artificial Neural Networks (ANN). As such, the book starts with the basics of ANN and different mathematical preliminaries concerning algebraic equations. Then it addresses ANN-based methods for solving different algebraic equations, viz. polynomial equations, diophantine equations, transcendental equations, a system of linear and nonlinear equations, eigenvalue problems etc., which are the basic equations to handle the application problems mentioned in the content of the book. Although various methods exist to address these problems, they may sometimes be problem dependent and fail to give a converged solution with particular discretization. Accordingly, ANN-based methods have been addressed here to solve these problems. Detailed ANN architecture with step-by-step procedure and algorithm have been included. Different example problems are solved concerning various applications and mathematical problems. Convergence plots and convergence tables of the solutions are depicted to show the efficacy of these methods. It is worth mentioning that various application problems, viz. Bakery problems, Power electronics applications, Pole placement, Electrical Network Analysis, Structural engineering problems etc., have been solved using the ANN-based methods