In the Present book Chapter – I is an introductory one. It contains the general introduction and statement of the problem of Latin squares. Chapter – II presents the Latin square theory along with the construction of different types of Latin squares. It also gives the description about the layout, analysis and various problems of Latin square design. Chapter – III describes the concept, construction and important application of orthogonal Latin squares. It contains the use of Galois filed in the construction of mutual orthogonal Latin squares. Chapter – IV depicts the various applications of Latin squares in the analysis of design of experiments. It gives the applications of Latin squares, in particular, orthogonal Latin squares in the construction of incomplete block designs such as BIBD, PBIBD., and Latin design. Chapter – V gives the conclusions .study. Some selected references are listed under title ‘BIBLIOGRAPHY’.