Designed primarily as a text for undergraduate and post-graduate students of statistics, the book introduces the readers to the fundamentals of Galois field and finite geometry. It lays emphasis on different aspects of construction of Design and Experiments with Projective geometry and Euclidian geometry. The book deals with the construction of mutually orthogonal latin squares (MOLS) and Hyper Graeco-Latin square and discusses construction of incomplete block design such as balanced incomplete block design (BIBD), partially balanced incomplete block design (PBIBD), including Lattice designs and -Designs based on Galois field. Besides, the book focuses on cofounding in factorial experiments, and it also describes quadratic residue as well as orthogonal arrays through Galois field. A separate chapter on Analysis of block design is included which contains some of the concepts developed recently.