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: β’ Statistical fluctuation formulae for the dielectric constant β’ Particle-Mesh-Ewald, Fast-Multipole-Method and image-based reaction field method for long-range interactions β’ High-order singular/hypersingular (NystrΓΆm collocation/Galerkin) boundary and volume integral methods in layered media for Poisson-Boltzmann electrostatics, electromagnetic wave scattering and electron density waves in quantum dots β’ Absorbing and UPML boundary conditions β’ High-order hierarchical NΓ©dΓ©lec edge elements β’ High-order discontinuous Galerkin (DG) and Yee finite difference time-domain methods β’ Finite element and plane wave frequency-domain methods for periodic structures β’ Generalized DG beam propagation method for optical waveguides β’ NEGF(Non-equilibrium Green's function) and Wigner kinetic methods for quantum transport β’ High-order WENO and Godunov and central schemes for hydrodynamic transport β’ Vlasov-Fokker-Planck and PIC and constrained MHD transport in plasmas