This oberseminar gives an introduction to the area of phylogenetic networks. The concept of a phylogenetic tree is well defined and it is assumed that students taking this course are familar with the topic of phylogenetic trees. The concept of a phylogenetic network, however, is not clearly defined and there is much confusion over the topic. The goal of this course is to give a systematic overview over the different approaches and concepts and will explore and highlight some of the connections between the different ideas.

Here is a rough list of contents:

0. Overview
1. On implicit and explicit networks
2. Split Networks
2.1 Distance methods
2.1.1 The four point condition
2.1.2 Buneman trees
2.1.3 The split decomposition
2.1.4 Neighbor-net
2.2 Sequence methods
2.2.1 Parsimony splits
2.2.2 Median networks
2.2.3 Spectral analysis and splits
2.3 Tree methods
2.3.1 Consensus trees
2.3.2 Consensus networks
2.3.3 Super networks and the Z-closure method

3. Reticulate Networks
3.1 Galled trees
3.2 Reticulations and SPRs
3.3. Reticulations and splits
3.4 Hybridization networks
3.5 Recombination networks
3.5.1 Ancestor recombination graphs
3.5.2 Branch-and bound approaches
3.5.3 Heuristics
3.6 Lower and Upper bounds

4. DLT Networks

5. Haplotype networks

6. Reticulgrams

7. Statistical Parsimony

8. Netting

9. Median joining networks