For any truncated path algebra Λ, we give a structural description of the modules in the categories
$${\mathcal{P}^{<\infty}(\Lambda\text{-}{\rm mod})}$$
and
$${\mathcal{P}^{<\infty}(\Lambda\text{-}{\rm mod})}$$
, consisting of the finitely generated (resp. arbitrary) Λ-modules of finite projective dimension. We deduce that these categories are contravariantly finite in Λ−mod and Λ-Mod, respectively, and determine the corresponding minimal
$${\mathcal{P}^{<\infty}}$$
-approximation of an arbitrary Λ-module from a projective presentation. In particular, we explicitly construct—based on the Gabriel quiver Q and the Loewy length of Λ—the basic strong tilting module Λ
T (in the sense of Auslander and Reiten) which is coupled with
$${\mathcal{P}^{<\infty}(\Lambda\text{-}{\rm mod})}$$
in the contravariantly finite case. A main topic is the study of the homological properties of the corresponding tilted algebra
$${\tilde{\Lambda} = {\rm End}_\Lambda(T)^{\rm op}}$$
, such as its finitistic dimensions and the structure of its modules of finite projective dimension. In particular, we characterize, in terms of a straightforward condition on Q, the situation where the tilting module
$${T_{\tilde{\Lambda}}}$$
is strong over
$${\tilde{\Lambda}}$$
as well. In this Λ-
$${\tilde{\Lambda}}$$
-symmetric situation, we obtain sharp results on the submodule lattices of the objects in
$${\mathcal{P}^{<\infty}({\rm Mod}\text{-}\tilde{\Lambda})}$$
, among them a certain heredity property; it entails that any module in
$${\mathcal{P}^{<\infty}({\rm Mod}\text{-}\tilde{\Lambda})}$$
is an extension of a projective module by a module all of whose simple composition factors belong to
$${\mathcal{P}^{<\infty}({\rm Mod}\text{-}\tilde{\Lambda})}$$
.
