ABSTRACT This nal project discusses the properties of BM-algebra and the relation of BM-algebra with BCI -algebra, BF-algebra and Coxeter algebra. Their rela- tionship is proven by showing that the properties of BM-algebra, BCI -algebra, BF-algebra, Coxeter algebra are interrelated. Keywords: BM-algebra, BCI -algebra, BF-algebra, Coxeter algebra.