0ur goal is to initiate (co)homology theory for quasigroups of Bol-Moufang. Our approach which has its roots in the work of Eilenberg and his coauthors (MacLane, Cartan) is to analyze extensions of a quasigroup $(X, *_X)$ by an affine quasigroup $(A, *_A)$ of the same type. We study these extensions not to classify them but to have the first glimpse at their homology via their second and third boundary operation, $\partial_2(x,y)$ and $\partial_3(x,y,z)$ respectively. We compute the second homology groups for all distinguishing examples of Bol-Moufang quasigroups described by Phillips and Vojtechovsky. We specualte about use of homology of Bol-Moufang quasigroups in Knot Theory. It is a joint work with Anthony Christiana, Ben Clingenpeel, Huizheng Guo, Jinseok Oh, and Anna Zamojska-Dzienio.