  We present an algorithmic classification of the irreps of the $N$-extended
one-dimensional supersymmetry algebra linearly realized on a finite number of
fields. Our work is based on the 1-to-1 \cite{pt} correspondence between
Weyl-type Clifford algebras (whose irreps are fully classified) and classes of
irreps of the $N$-extended 1D supersymmetry. The complete classification of
irreps is presented up to $N\leq 10$. The fields of an irrep are accommodated
in $l$ different spin states. N=10 is the minimal value admitting length $l>4$
irreps. The classification of length-4 irreps of the N=12 and {\em real} N=11
extended supersymmetries is also explicitly presented.\par Tensoring irreps
allows us to systematically construct manifestly ($N$-extended) supersymmetric
multi-linear invariants {\em without} introducing a superspace formalism.
Multi-linear invariants can be constructed both for {\em unconstrained} and
{\em multi-linearly constrained} fields. A whole class of off-shell invariant
actions are produced in association with each irreducible representation. The
explicit example of the N=8 off-shell action of the $(1,8,7)$ multiplet is
presented.\par Tensoring zero-energy irreps leads us to the notion of the {\em
fusion algebra} of the 1D $N$-extended supersymmetric vacua.
