The purpose of my fellowship application at the KLI is to write-up my PhD thesis entitled “Network Models of Tetrapod Skull Morphology: Implications for the analysis of morphological integration, modularity, and phenotypic stability”, which has been developed under supervision of Diego Rasskin-Gutman at the Theoretical Biology Research Group, in the Institute Cavanilles for Biodiversity and Evolutionary Biology of the University of Valencia. The main goal of my thesis project is to use a network theory framework to study morphological problems related to form at the connectivity level. Specifically, I have built anatomical network models for a sample of tetrapod skulls, on which I performed a comparative analysis of morphological integration and modularity. For this purpose, prior to any empirical study I offer a conceptual anatomical interpretation of those parameters specific to the network theory, in order to discuss properly all possible findings. The analysis of evolutionary trends in the morphological complexity of the skull is the second goal of my project. The classical trend toward reduction of skull bone number in vertebrates is studied from the perspective of the skull as a network. Here, I discuss a trend in increase of complexity and integration in skull network, as well as an evolutionary pattern in symmetry acquisition due to emergence of new unpaired bones. Finally, I use the information obtained from different network null models to build the theoretical morphospace (i.e. connectospace) of the tetrapod skull. The results of this four years work led me to propose several hypotheses about tetrapod skull organization, as an integrative and modular system, as well as to offer some clues about how the particular network organization of skull bones affects the morphology of the skull during development and evolution. For example, the key role of highly connected bones in the maintenance of skull robustness to bone loss and fusions events during evolution, the changes in skull modules symmetry due to unpaired bones, and the whole network pattern as a correlation map underlying shape covariations.