More specifically, there are (Dress, A. et al, Basic Phylogenetic Combinatorics, Cambridge University Press. 2012) three principal options for encoding phylogenetic trees: split systems, quartet systems, and metrics. Such encodings provide useful options for analyzing and manipulating phylogenetic trees and networks, and they are at the basis of much of phylogenetic data processing. In the lectures, it will be explained how each of these three encodings provides a unique perspective for viewing, perceiving, and analysing the combinatorial structure of a phylogenetic tree and how they are interrelated (see the figure).

In the first lecture, X-trees and X-networks will be introduced and biologically relevant examples will be provided. Next, it will be described how X-trees give rise to metrics, quartet systems and split systems over X and those quartet or split systems or metrics over X that correspond to an X-tree will be characterized in terms of simple combinatorial conditions (Lecture 2 and 3). And then, as "naturally" obtained quartet or split systems or metrics rarely satisfy these conditions, the problem of how to deal best with data that do not simply correspond to an X-tree will be addressed (Lecture 4 to 6).