The modern day power grid is a highly complex system; as such, maintaining stable operations of the grid relies on many factors. Additionally, the increased usage of renewable energy sources significantly complicates matters. Attempts to assess the current stability of the grid make use of several key parameters, however obtaining these parameters to make an assessment has its own challenges. Due to the limited number of measurements and the unavailability of information, it is often difficult to accurately know the current value of these parameters needed for stability assessment. This work attempts to estimate three of these parameters: the Inertia, Topology, and Voltage Phasors. Without these parameters, it is no longer possible to determine the current stability of the grid. Through the use of machine learning, empirical studies, and mathematical optimization it is possible to estimate these three parameters when previously this was not the case. These three methodologies perform estimations through measurement-based approaches. This allows for the obtaining of these parameters without required system knowledge, while improving results when systems information is known. / Ph. D.