In this minicourse I will give a series of examples illustrating how geometric and topological ideas arise in neuroscience. First, I'll tell you about some interesting neurons, such as place cells and grid cells, and the topology associated to their neural activity. I will also explain how convex neural codes capture additional features of the stimulus space, such as intrinsic dimension. Second, I'll explain how the statistics of persistent homology can be used to detect - or reject - geometric organization in neural activity data, using examples from hippocampus and olfaction. In the third and final talk, I'll transition to studying attractor neural networks, where we will see how network dynamics are determined by combinatorial features of special network motifs and their embeddings in the larger network.