Empirical strategies for the study of morphological organization have not developed as much as those for evolutionary studies such as phylogenetics, population genetics, and the theory of natural selection. The next challenge for biology requires mending this deficiency in order to understand organization at the organismal level. The main objective of this project is to search for suitable methodological strategies to deal with the study of the morphological evolution of the vertebrate skull. The skull is one of the most conservative complexes in vertebrate design because cranial architecture is regulated by the dynamics of the nervous system. In this project I will explore the invariant rules that uphold the geometry of the mammalian skull: Can we ever recognize any mammalian skull? Do mammals follow a geometry distinct from that of reptiles? Is this geometry violated in human teratologies? The geometrical and disparity patterns of the mammalian skull will be formalized by means of empirical tools (i.e., morphometrics) that will then be integrated within theoretical morphospaces. The combination of empirical and theoretical morphospaces will be used to explore the morphogenetic and macroevolutionary dimensions of shaping life against hypotheses that support that morphology is due to historical contingencies throughout geological time. It is expected that major groups such as Archosauria or Mammalia will show a set of general geometrical rules (viz., proportions, symmetries, and conncestions) delimiting morphological boundaries at macroevolutionary levels, as a consequence of the regulative processes that occur during development.