A unique and comprehensive graduate text and reference on numerical methods for electromagnetic phenomena, from atomistic to continuum scales, in biology, optical-to-micro waves, photonics, nanoelectronics and plasmas. The state-of-the-art numerical methods described include: * Statistical fluctuation formulae for the dielectric constant * Particle-Mesh-Ewald, Fast-Multipole-Method and image-based reaction field method for long-range interactions * High-order singular/hypersingular (Nystrom collocation/Galerkin) boundary and volume integral methods in layered media for Poisson-Boltzmann electrostatics, electromagnetic wave scattering and electron density waves in quantum dots * Absorbing and UPML boundary conditions * High-order hierarchical Nedelec edge elements * High-order discontinuous Galerkin (DG) and Yee finite difference time-domain methods * Finite element and plane wave frequency-domain methods for periodic structures * Generalized DG beam propagation method for optical waveguides * NEGF(Non-equilibrium Green's function) and Wigner kinetic methods for quantum transport * High-order WENO and Godunov and central schemes for hydrodynamic transport * Vlasov-Fokker-Planck and PIC and constrained MHD transport in plasmas