  Both the original Temperley-Lieb algebras $\mathsf{TL}_{n}$ and their dilute
counterparts $\mathsf{dTL}_{n}$ form families of filtered algebras:
$\mathsf{TL}_{n}\subset \mathsf{TL}_{n+1}$ and
$\mathsf{dTL}_{n}\subset\mathsf{dTL}_{n+1}$, for all $n\geq 0$. For each such
inclusion, the restriction and induction of every finite-dimensional
indecomposable module over $\mathsf{TL}_{n}$ (or $\mathsf{dTL}_{n}$) is
computed. To accomplish this, a thorough description of each indecomposable is
given, including its projective cover and injective hull, some short exact
sequences in which it appears, its socle and head, and its extension groups
with irreducible modules. These data are also used to prove the completeness of
the list of indecomposable modules, up to isomorphism. In fact, two
completeness proofs are given, the first is based on elementary homological
methods and the second uses Auslander-Reiten theory. The latter proof offers a
detailed example of this algebraic tool that may be of independent interest.
