This book presents a detailed analytical and computational electromagnetic (CEM) treatment of guided electromagnetic (EM) wave propagation in independently time-varying dielectric medium, using the finite-difference time-domain (FDTD) simulation technique.   The contents provide an extensive literature review, explaining the importance of time-varying media (temporal photonic crystals) in new  exotic applications that involve rich EM phenomena such as parametric amplification, frequency conversion, non-reciprocal gain, electromagnetic energy accumulation, temporal coating and temporal  aiming  (beam-forming).  A  one-dimensional  (1D) FDTD simulation paradigm is then formulated in this book, starting from Maxwells equations and boundary  conditions.  The  issues  of  hard/soft  source  realizations,  perfectly matched layers  (PMLs),  choice  of  simulation  parameters  (cell-size  and  time-stepping)  are  thoroughly explained  through  new  visualization  tools.   This book provides a unique combination of rigorous analytical  techniques, several FDTD simulation examples with reproducible  source-codes, and new visualization/post-processing mechanisms.  The contents of this book should prove to be useful for students, research scholars, scientists and engineers, working in the field of applied electromagnetics, and aiming to design cutting-edge microwave/optical devices based on time-varying medium.