The first book to make an appearance that explicitly deals with phylogenetic networks was:
D. H. Huson, R. Rupp and C. Scornavacca (2011) Phylogenetic Networks: Concepts, Algorithms and Applications. Cambridge University Press. [Dated 2010 but published January 17 2011] Available in hardback ISBN:978-0-521-75596-2 and as an eBook ISBN:978-0-511-92242-8.
In addition to the three reviews that appear as part of the publisher's blurb, a number of independent book reviews have appeared since its publication:
Tiratha Raj Singh (2011) Current Science 100: 1570-1571.
Paul Cull (2011) Computing Reviews Review#139416.
Steven Kelk (2012) Systematic Biology 61: 174-175.
Jim Whitfield (2012) Systematic Biology 61: 176-177.
These are all worth reading, but I wish to comment here on one particular review, the one by Steven Kelk. This review makes two points about current network methods that seem to me not to have been sufficiently emphasized in other publications. The review itself is thus an important contribution to the literature on phylogenetic networks.
(1) Rooted networks based on a "hybridization" model can be derived by combining clusters, triplets or trees. [Note: combining characters usually leads to a "recombination" model.] However, only by combining trees do the reticulation vertices in the resulting network explicitly model reticulate evolutionary events (e.g. hybridization or horizontal gene transfer); for clusters and triplets the reticulation vertices can be abstract. This has important practical consequences for biologists, who routinely interpret rooted networks as though all of the vertices (nodes) represent inferred ancestors undergoing "descent with modification" (as Charles Darwin called it). There has been insufficient attention paid to this point in the literature on cluster and triplet methods.
Note that this point does not deny any intrinsic mathematical interest in clusters and triplets (which Steven, himself, emphasizes in his own research work). Nor does it deny any possible use of them in practical network methods; indeed, I have seen them work quite well in practice. The point is simply that the tree model explicitly provides something that biologists find valuable, and which (I would argue) has been principally responsible for the widespread use of that model in phylogenetics. One can even argue that phylogenetic analysis is the inference of vertices in a tree/network. (If you look at Darwin’s only published tree you will note that it is the vertices of his tree that are missing, indicating his explicit doubt about the feasibility of inferring them.)
(2) Great attention has been paid in the literature to certain topologically restricted sub-families of rooted networks (such as galled networks, level-k networks, etc). These theoretical classes have been chosen because of concerns about computational tractability, rather than anything to do with the priorities of biological modeling. Unfortunately, little attention has been paid to how likely these networks are from the biological viewpoint. Perhaps the only other unequivocal publication on this topic is that of (M. Arenas, M. Patricio, D. Posada, G. Valiente. 2010. Characterization of phylogenetic networks with NetTest. BMC Bioinformatics 11: 268) More work needs to be done to address this uncertain applicability.
Steven's review appeared in Systematic Biology, which actually has a long tradition of original book reviews that are worth citing in formal research publications. For example, one of the more highly cited papers in the journal is the book review in which Don Colless published his tree-imbalance formula (D.H. Colless. [Review of] Phylogenetics: the Theory and Practice of Phylogenetic Systematics. Systematic Zoology 1982, 31:100-104), which receives continual citation because the formula is still commonly used today. Not everyone publishes original research in their book reviews!
Declaration of potential competing interest: I am currently the Book Review Editor for Systematic Biology, and so I am the one who commissioned Steven's review. However, I take no credit for the contents of the review! The numerous reviewers I have dealt with over the years have produced reviews that varied from excellent through mediocre to ones that needed extensive revision, and on to two that I wrote myself when the original reviewer failed to deliver.