Textual criticism is the discipline that aims to reconstruct the texts of ancient works from their surviving copies. Even though modern textual criticism has been practiced for nearly two centuries, no comprehensive mathematical formalization of its goals and logic has been developed to date. This paper provides a systematization of the main intuitions that form the basis of the discipline. Basic concepts like "manuscript", "witness", "collation", "textual unit" and "reading", among others, are first defined and then used to create more complex textual-transmissional constructs, like the notions of local and non-local genealogies, archetypes, contamination, conflations, evolutions, and retroversions. We also formalize the task of a textual critic in terms of probability spaces. In order to showcase the expressive potential of the model, we use it to provide definitions of three common Lachmannian heuristics (stemmata codicum, local stemmata, and variant stemmata), as well as a framework for understanding majority rules. Moreover, we describe the model's potential for allowing researchers to fully specify and develop computer simulations in an internally consistent way. The present mathematical formulation offers a way to mathematically characterize the textual transmission of works and the various strategies that could be leveraged to recuperate their original wordings. It can benefit textual critics by providing increased rigor in discussions about variants and also by facilitating the creation of new computational methods and software packages.