This chapter presents the fundamentals of the finite-difference time-domain (FDTD) method, in which the formulation is provided for the case of linear, isotropic and lossless media. In addition to the traditional explicit FDTD method, also given are the formulations of the implicit FDTD methods based on the Crank–Nicolson (CN), alternating-direction implicit (ADI), and locally one-dimensional (LOD) schemes. Some alternative techniques for implementing implicit FDTD method are provided. Furthermore, the hybrid implicit-explicit (HIE) FDTD method is explained, which is also attractive for the problem where small meshes are required only in the specific direction. The application of the absorbing boundary condition is quite important for the practical use of the FDTD method. The formulation of the convolutional perfect matched layer (CPML) is given, which is used throughout this book.