Perception depends upon the coordinated activity of populations of neurons. Howneural populations represent structure in the outside world through their activity is an important open question. One approach to this problem is the concept of the receptive field, which quantifies how external stimulation modulates the activity of individual neurons. While receptive fields are a powerful concept for the experimenter, the brain itself does not have access to its own receptive fields. This dissertation applies methods from the field of algebraic topology to characterize the structure of neural population activity in the secondary auditory region NCM of the European starling. Chapter 2 demonstrates that the simplicial complex associated to population activity in NCM carries behaviorally-relevant information xiiabout learned categories. Along the way, a new similarity measure for population activity is developed, called the Simplicial Laplacian Spectral Entropy. It is shown that this measure quantifies the similarity of simplicial complexes associated with neural activity in a way that depends upon their global topological structure. Chapter 3 explores the connection between neural topology and classical receptive fields, by showing that the intrinsic geometry of the population activity matches the geometry of the receptive fields. This shows that the temporal coativity structure of the population contains a direct representation of the stimulus structure without requiring explicit computation of receptive fields. This validates a previously described theoretical mechanism in a sensory system for the first time in-vivo, and provides a new understanding for population activity in sensory regions. This chapter also introduces a technique for reconstructing acoustic spectrograms of complex, natural vocal signals from neural activity, which will be a powerful technique for exploring population level representations in future studies. The final chapter of this dissertation describes a new mathematical description of the phenomenon of polychronization in spiking neural networks. This serves as a bridge between the experimental results of this dissertation and a theoretical understanding of the emergence of spatiotemporal structure in the activity of neural populations.