In this book, Maxwell's equations are solved in the frequency domain using FDFD. The implementation of the method is verified by comparing its results by theoretical and experimental published results for 2-D and 3-D problems. The particle swarm optimization technique is discussed in this book as an optimization technique used in the inverse problems. The first application of the hybrid method from FDFD/PSO methods in this book is the breast cancer detection. 2-D and 3-D models for the breast are used. The models include randomly distributed fatty breast tissue, glandular tissues, skin, as well as chest wall. The position and the size of the malignant tissue are depicted in 2-D and 3-D domains. The second application is the crack detection in the conductor and dielectric objects. The crack position, width and depth have been obtained in single and multilayer dielectric objects. Also, multiple cracks on the object are illustrated. FDFD is used to analyze metamatrials and chiral materials. The implementation of the method for these materials is verified by comparing its results by theoretical and experimental published ones. The final application in this book is the minimizat