Phylogenetics is the study of how different groups (taxa, singular taxon) of living things are related to one another, taxonomy is the naming and classifying of taxa, and systematics is a combination of both: the classification of life based on phylogenetic relationships. In short, we recover evolutionary trees (phylogenies, singular phylogeny; often depicted in a branching tree-like diagram called a cladogram) by using computer algorithms to figure out which taxa have more in common with one another than they do with other taxa. If two taxa have more in common with one another than with any other taxon, they are sisters, and share a more recent common ancestor with one another than either does with any other taxon. In modern (extant) organisms, we can look for molecular (e.g., DNA) similarities, but with extinct things we are, for the most part, restricted to using morphology (the shapes of bones and other structures that preserve as fossils). To do this, we build phylogenetic matrices (singular matrix).
A matrix has two primary components: taxa (rows) and characters (columns). Characters are variable traits, which we score into the matrix for each specimen using codes for the different character states. Character states are the different versions of a character; for example, eye color is a character, and the different colors themselves (brown, blue, green, etc.) are the states. Codes are numerical representations (0, 1, 2, etc.) of character states so that the algorithms can read the data, and scoring is the act of entering codes into the matrix for each specimen. Once your matrix is built, you're ready to analyze it using a phylogenetic algorithm of your choice and recover a phylogeny!
Of course, there is a lot more to it than that, which is why I've added the following two papers. Compleat Cladist will help you get started with phylogenetics more broadly, and when you're ready to do a deeper dive into how to create characters, head over to Simões et al. 2017.
These are two works that I consider to be critical for understanding mosasaur anatomy and phylogeny. The first is Russell 1967, a comprehensive review of the anatomy and functional morphology of all North American mosasaurs known at the time. The second is Bell 1997, the first analysis of mosasaur phylogeny using modern phylogenetic systematics. This character list is still the backbone of most analyses of mosasaur relationships analyzed today, and there are many great figures showing characters and their states across different mosasaurs.
Finally, if you are itching to learn about the history of Western Interior Seaway fossil collection and even more about mosasaurs and the other animals they shared their world with, Oceans of Kansas is without equal.
These are just a few papers that take a bigger-picture look at two of the most common kinds of mosasaurs, Mosasaurus and Tylosaurus. Jiménez & Caldwell 2019 is a review of tylosaurine phylogeny, and my own work (Zietlow 2020) is a deep dive into intraspecific variation in a few Tylosaurus species, with a review of all the literature I could find at the time that is relevant to mosasaur ontogeny (growth & development). Finally, Street & Caldwell 2017 is a revision of Mosasaurus hoffmannii, the first mosasaur that was scientifically described.
We're super lucky to have multiple mosasaur fossils that preserve soft tissue, including scale impressions and the outlines of their fins! Both are described in the first two papers, Konishi et al. 2012 and Lindgren et al. 2o13.
We also have fossils that show some pretty hardcore evidence of mosasaurs attacking each other! Everhart 2008 provides a review of several of these fossils, including the gnarliest of them all: the holotype skull of Tylosaurus kansasensis, which is loaded with wicked unhealed gouges and has a broken neck.
At the end of the day, mosasaurs are just big dead wet lizards! If you're interested in learning more about squamates (lizards + snakes) more generally, Simões & Pyron 2021 provide a very comprehensive review about how our understanding of squamates has become what it is today. If you're looking for a detailed, recent molecular analysis of squamate phylogeny, head over to Burbrink et al. 2020. If morphology is more your jam, check out Oelrich 1956 for a detailed discussion of iguanian head anatomy. Finally, if you're interested in learning about how lizards develop as embryos, Griffing et al. 2019 is a great starting point.
Last, but certainly not least: it wouldn't be a mosasaur library if we didn't cover quadrates! The quadrate bone is a critically important part of the lizard skull; it connects the lower jaws to the rest of the skull, contributes to skull kinesis (flexibility), and is involved in hearing (in mammals, the incus is the same bone, just super reduced and located inside the middle ear).
For mosasaurs, quadrates are highly diagnostic: basically what this means is that if a mosasaur fossil only preserves one bone, and that bone is the quadrate, you have a pretty good chance of being able to identify it down to the genus (or, in some cases, species) level.
Palci et al. 2019 provides a review of quadrate bones across all squamates, and Palci et al. 2021 focuses exclusively on mosasaur quadrates. Finally, Paluh et al. 2018 discuss how quadrate bone shape varies (or doesn't!) within a single species.
Left quadrate of Tylosaurus FHSM VP-3366