This chapter introduces the Finite Element Method (FEM) as a variational-based technique for solving differential equations, emphasizing its applications in fluid mechanics, heat transfer, and acoustics. The book, authored by J. N. Reddy, is structured into five chapters and includes three computer programs. The initial chapter provides an overview and historical context, while the second chapter delves into the variational formulation and approximation methods. The third chapter focuses on one-dimensional second-order equations, discussing error sources and numerical integration schemes. The fourth chapter covers two-dimensional problems, including mesh generation and isoparametric elements. The final chapter touches on advanced topics such as eigenvalue problems and nonlinear dynamics. The reviewer recommends the book as a comprehensive introduction to FEM, suggesting expansions in the three-dimensional section and additional topics like wave front and subspace iteration.This chapter introduces the Finite Element Method (FEM) as a variational-based technique for solving differential equations, emphasizing its applications in fluid mechanics, heat transfer, and acoustics. The book, authored by J. N. Reddy, is structured into five chapters and includes three computer programs. The initial chapter provides an overview and historical context, while the second chapter delves into the variational formulation and approximation methods. The third chapter focuses on one-dimensional second-order equations, discussing error sources and numerical integration schemes. The fourth chapter covers two-dimensional problems, including mesh generation and isoparametric elements. The final chapter touches on advanced topics such as eigenvalue problems and nonlinear dynamics. The reviewer recommends the book as a comprehensive introduction to FEM, suggesting expansions in the three-dimensional section and additional topics like wave front and subspace iteration.