This book presents recent advances in computational electromagnetics, focusing on fast and efficient algorithms. It is edited by Weng Cho Chew, Jian-Ming Jin, Eric Michielssen, and Jiming Song. The book covers a wide range of topics, including fast multipole methods (FMM), multilevel fast multipole algorithm (MLFMA), error analysis, perfectly matched layers (PML), and other computational techniques for solving electromagnetic problems. The book begins with an introduction to electromagnetic analysis and computational electromagnetics, discussing the evolution of the field and recent fast algorithms. It then explores the two-dimensional FMM and MLFMA, including interpolation, truncation, and integration errors, as well as their relation to group theory. The three-dimensional version of FMM and MLFMA is also discussed, along with their application to real-world problems and parallelization on shared-memory machines. The book then addresses the low-frequency solution of Maxwell's equations using fast algorithms, discussing the treatment needed for FMM and MLFMA to prevent their catastrophic breakdown at low frequencies. It also describes a method to apply the LF-MLFMA based on different basis functions. The chapter on error analysis of surface integral equation methods discusses discretization and integration errors, as well as the deconditioning of the matrix equation by the method of moments. The book also covers the theory of perfectly matched layers (PML), including their generalization to curvilinear coordinates and complex media, and discusses stability issues related to PML. It addresses the efficient solution of forward and inverse problems for buried objects using FFT-based methods, and discusses recent advances in different inversion algorithms. The book touches upon solving the penetrable problem at very low frequencies, discussing the low-frequency problem encountered in metallic objects and how it also occurs for dielectric and lossy material objects. It describes a way to solve this problem so that the solution of integral equations remains stable all the way from zero frequency to microwave frequencies. The book describes an algorithm to solve three-dimensional waveguide structures using numerical mode matching, but using the finite difference method. It also discusses the use of the spectral Lanczos decomposition method to find the modes. The chapter addresses the problem of solving the volume integral equation concurrently with the surface integral equation, and demonstrates how the solutions are accelerated with MLFMA. The book also covers solving axially symmetric, body-of-revolution (BOR) geometry using the finite element method (FEM), reducing a three-dimensional problem to two dimensions, and discusses the practical use of cylindrical PML for truncating the FEM mesh. It also considers the treatment of BOR geometry with appendages. The book reports on hybridization in computational electromagnetics, discussing hybridization between FEM and the absorbing boundary condition (ABC), boundary integral equation (BIE), MLFMA, adaptive absorbing boundary condition (AABC), and shooting and bouncing ray (SBR). It also considers hybridization between MOM and SThis book presents recent advances in computational electromagnetics, focusing on fast and efficient algorithms. It is edited by Weng Cho Chew, Jian-Ming Jin, Eric Michielssen, and Jiming Song. The book covers a wide range of topics, including fast multipole methods (FMM), multilevel fast multipole algorithm (MLFMA), error analysis, perfectly matched layers (PML), and other computational techniques for solving electromagnetic problems. The book begins with an introduction to electromagnetic analysis and computational electromagnetics, discussing the evolution of the field and recent fast algorithms. It then explores the two-dimensional FMM and MLFMA, including interpolation, truncation, and integration errors, as well as their relation to group theory. The three-dimensional version of FMM and MLFMA is also discussed, along with their application to real-world problems and parallelization on shared-memory machines. The book then addresses the low-frequency solution of Maxwell's equations using fast algorithms, discussing the treatment needed for FMM and MLFMA to prevent their catastrophic breakdown at low frequencies. It also describes a method to apply the LF-MLFMA based on different basis functions. The chapter on error analysis of surface integral equation methods discusses discretization and integration errors, as well as the deconditioning of the matrix equation by the method of moments. The book also covers the theory of perfectly matched layers (PML), including their generalization to curvilinear coordinates and complex media, and discusses stability issues related to PML. It addresses the efficient solution of forward and inverse problems for buried objects using FFT-based methods, and discusses recent advances in different inversion algorithms. The book touches upon solving the penetrable problem at very low frequencies, discussing the low-frequency problem encountered in metallic objects and how it also occurs for dielectric and lossy material objects. It describes a way to solve this problem so that the solution of integral equations remains stable all the way from zero frequency to microwave frequencies. The book describes an algorithm to solve three-dimensional waveguide structures using numerical mode matching, but using the finite difference method. It also discusses the use of the spectral Lanczos decomposition method to find the modes. The chapter addresses the problem of solving the volume integral equation concurrently with the surface integral equation, and demonstrates how the solutions are accelerated with MLFMA. The book also covers solving axially symmetric, body-of-revolution (BOR) geometry using the finite element method (FEM), reducing a three-dimensional problem to two dimensions, and discusses the practical use of cylindrical PML for truncating the FEM mesh. It also considers the treatment of BOR geometry with appendages. The book reports on hybridization in computational electromagnetics, discussing hybridization between FEM and the absorbing boundary condition (ABC), boundary integral equation (BIE), MLFMA, adaptive absorbing boundary condition (AABC), and shooting and bouncing ray (SBR). It also considers hybridization between MOM and S