  Motivated by using combinatorics to study jets of monomial ideals, we extend
a definition of jets from graphs to clutters. We offer some structural results
on their vertex covers, and show an interesting connection between the cover
ideal of the jets of a clutter and the symbolic powers of the cover ideal of
the original clutter. We use this connection to prove that jets of very
well-covered graphs are very well-covered. Next, we turn our attention to
principal jets of monomial ideals, describing their primary decomposition and
minimal generating sets. Finally, we give formulas to compute various algebraic
invariants of principal jets of monomial ideals, including their Hilbert
series, Betti numbers, multiplicity and regularity.
