Anesthesia, while a highly useful clinical entity, is a very poorly understood phenomenon. Although the receptor level actions of general anesthetic agents are well characterized, the ability to integrate these molecular-level effects into an understanding of systems-level effects such as the biphasic effect and anesthetic hysteresis is limited and incomplete. My research in this area aims to bridge this explanatory gap and set the stage for improved understanding of the anesthetic state as well as its neural substrate and observables. To this end I utilize the tools of computational neuroscience, theoretical physics (e.g. statistical mechanics), nonlinear dynamics, and stochastics applied to single neuron modelling of the effects of anesthetic agents at varying degrees of model abstraction. The single neuron represents an underdeveloped area of inquiry in the computational neuroscience of anaesthetic effect and a link between experimental investigations at the molecular level and mesoscopic mean-field theories at the whole cortex level. The integration of anesthetic effect into other, more abstract modelling paradigms as well as biophysically grounded paradigms such as the mean-field approach is also an area of investigation. This research involves the implementation of model simulations in the Matlab programming environment and requires some degree of understanding of basic calculus.