  In this article we develop a new way of systematically constructing
infinitely many families of smooth subvarieties $X$ of any given dimension $m$,
$m \geq 3$, and any given codimension in $\mathbb P^N$, embedded by complete
subcanonical linear series, and, in particular, in the range of Hartshorne's
conjecture. We accomplish this by showing the existence of everywhere
non--reduced schemes called ropes, embedded in $\mathbb P^N$, and by smoothing
them. In the range $3 \leq m < N/2$, we construct smooth subvarieties, embedded
by complete subcanonical linear series, that are not complete intersections. We
also go beyond a question of Enriques on constructing simple canonical surfaces
in projective spaces, and construct simple canonical varieties in all
dimensions. The canonical map of infinitely many of these simple canonical
varieties is finite birational but not an embedding. Finally, we show the
existence of components of moduli spaces of varieties of general type (in all
dimensions $m$, $m \geq 3$) that are analogues of the moduli space of curves of
genus $g > 2$ with respect to the behavior of the canonical map and its
deformations. In many cases, the general elements of these components are
canonically embedded and their codimension is in the range of Hartshorne's
conjecture.
