  The B-quadrilateral lattice (BQL) provides geometric interpretation of Miwa's
discrete BKP equation within the quadrialteral lattice (QL) theory. After
discussing the projective-geometric properties of the lattice we give the
algebro-geometric construction of the BQL ephasizing the role of Prym varieties
and the corresponding theta functions. We also present the reduction of the
vectorial fundamental transformation of the QL to the BQL case.
