  The index of a Lie algebra is an important algebraic invariant, but it is
notoriously difficult to compute. However, for the suggestively-named seaweed
algebras, the computation of the index can be reduced to a combinatorial
formula based on the connected components of a "meander": a planar graph
associated with the algebra. Our index analysis on seaweed algebras requires
only basic linear and abstract algebra. Indeed, the main goal of this
survey-type article is to introduce a broader audience to seaweed algebras with
minimal appeal to specialized language and notation from Lie theory. This said,
we present several results that do not appear elsewhere and do appeal to more
advanced language in the Introduction to provide added context.
