The theory of loops (groups without associativity), though researched by several mathematicians has not found a sound expression, for books, be it research level or otherwise, solely dealing with the properties of loops are absent. This is in marked contrast with group theory where books are abundantly available for all levels: as graduate texts and as advanced research books. The only three books available where the theory of loops are dealt with are: R. H. Bruck, A Survey of Binary Systems, Springer Verlag, 1958 recent edition (1971); H. O. Pflugfelder, Quasigroups and Loops: Introduction, Heldermann Verlag, 1990; Orin Chein, H. O. Pflugfelder and J.D.H. Smith (editors), Quasigroups and Loops: Theory and Applications, Heldermann Verlag, 1990. But none of them are completely devoted for the study of loops