I am learning about phylogenetic trees, but it is difficult for me to find some documents/books focused on the mathematics. I found Pachter & Sturmfels's article1, which is quite good, to be honest, but I would like to have something else. The phylogenetic trees use algebra as well as hidden Markov models (which if somebody knows a good article it is also welcome).
1 Lior Pachter, Bernd Sturmfels, The Mathematics of Phylogenomics, 2004.
Baez and Otter have an article that assembles phylogenetic trees into an operad and also say something about how Markov models used to reconstruct such trees can be interpreted as a type of algebraic structure.
Billera, Holmes, and Vogtmann have a paper on the geometry of the space of phylogenetic trees, showing that it can be given the structure of a $CAT(0)$ space, etc. I think there has been some interesting follow-up to their work, for example in tropical geometry.
(Disclaimer: I don't think these are the best places to learn about phylogenetic trees from an applied perspective. But "pure" mathematicians might find them interesting applications of some of the rather abstract things they study.)