Real world systems are complex, dynamic and exist across multiple scales. Recent revolutions in data collection and storage have provided researchers with unprecedented access to information about these systems in greater detail and variety than ever before. It is therefore imperative that we develop models and methods that are able to describe and detect changes in these systems through time and across scales. In this dissertation, I present work integrating multilayer networks and computational topology to perform multi-scale analysis of brain activity in epileptic mice. First, I present work providing theoretical advances to multilayer network theory. I prove that multilayer networks suffer from a resolution limit that prevents a popular method of community detection from detecting changes in community structure across layers of the network. I then propose an improvement to the multilayer network model that is more intuitive and helps mitigate the constraints of the resolution limit. Next, I describe work drawing from the tools of topological data analysis using persistent homology to localize and segment cells in biomedical images. Finally, I employing tools from computational topology and multilayer networks to study the evolution of neuronal dynamics in the brains of epileptic mice in the period leading up to seizure. This intricate, multi-scale analysis of brain dynamics enables us to identify evolving functional groups of neurons that drive the progression to a seizure.