  This note presents the Hilbert series technique to a wider audience in the
context of constructing group-invariant Lagrangians. This technique provides a
fast way to calculate the number of operators of a specified mass dimension for
a given field content, and is a useful cross check on more well-known group
theoretical methods. In addition, at least when restricted to invariants
without derivatives, the Hilbert series technique supplies a robust way of
counting invariants in scenarios which, due to the large number of fields
involved or to high dimensional group representations, are intractable by
traditional methods. We work out several practical examples.
