  The Tutte polynomial of a graph or a matroid, named after W. T. Tutte, has
the important universal property that essentially any multiplicative graph or
network invariant with a deletion and contraction reduction must be an
evaluation of it. The deletion and contraction operations are natural
reductions for many network models arising from a wide range of problems at the
heart of computer science, engineering, optimization, physics, and biology.
Even though the invariant is #P-hard to compute in general, there are many
occasions when we face the task of computing the Tutte polynomial for some
families of graphs or matroids. In this work we compile known formulas for the
Tutte polynomial of some families of graphs and matroids. Also, we give brief
explanations of the techniques that were use to find the formulas. Hopefully,
this will be useful for researchers in Combinatorics and elsewhere.
