%0 Journal Article %T Adventures in Invariant Theory %A P. D. Jarvis %A J. G. Sumner %J Mathematics %D 2012 %I arXiv %R 10.1017/S1446181114000327 %X We provide an introduction to enumerating and constructing invariants of group representations via character methods. The problem is contextualised via two case studies arising from our recent work: entanglement measures, for characterising the structure of state spaces for composite quantum systems; and Markov invariants, a robust alternative to parameter-estimation intensive methods of statistical inference in molecular phylogenetics. %U http://arxiv.org/abs/1205.5433v2