  Let $\Lambda$ be a finite-dimensional associative algebra. The torsion
classes of $mod\, \Lambda$ form a lattice under containment, denoted by $tors\,
\Lambda$. In this paper, we characterize the cover relations in $tors\,
\Lambda$ by certain indecomposable modules. We consider three applications:
First, we show that the completely join-irreducible torsion classes (torsion
classes which cover precisely one element) are in bijection with bricks.
Second, we characterize faces of the canonical join complex of $tors\, \Lambda$
in terms of representation theory. Finally, we show that, in general, the
algebra $\Lambda$ is not characterized by its lattice $tors\, \Lambda$. In
particular, we study the torsion theory of a quotient of the preprojective
algebra of type $A_n$. We show that its torsion class lattice is isomorphic to
the weak order on $A_n$.
