  Since the introduction of the concept of isotopism of algebras by Albert in
1942, a prolific literature on the subject has been developed for distinct
types of algebras. Nevertheless, there barely exists any result on the problem
of distributing Lie algebras into isotopism classes. The current paper is a
first step to deal with such a problem. Specifically, we define a new series of
isotopism invariants and we determine explicitly the distribution into
isotopism classes of $n$-dimensional filiform Lie algebras, for $n\leq 7$. We
also deal with the distribution of such algebras into isomorphism classes, for
which we confirm some known results and we prove that there exist $p+8$
isomorphism classes of seven-dimensional filiform Lie algebras over the finite
field $\mathbb{F}_p$ if $p\neq 2$.
