Part B (of a project involving four Parts) is about "bases of lines", a concept introduced by C. Herrmann and the author in the late 80's. Bases of lines attempt to describe a given modular lattice in a geometric way akin to how projective geometries describe complemented modular lattices. This e.g. yields the result that each modular lattice L of finite length d(L), and having s(L) many maximal congruences, has at least 2d(L)-s(L) many join-irreducible elements. Furthermore, an algorithm is proposed that calculates, in a compressed way, the (full) submodule lattice Sub(W) of any (sufficiently known) finite R-module W.