The results of a quantitative approach to the elucidation of the structure of the limbic system of the brain are presented. Total neuron populations and anatomically significant subpopulations of the medial and lateral mammillary nuclei of cat brain are determined. The subpopulations are measured by placing ultrasonic lesion arrays in efferent and afferent tracts and in associated nuclei, waiting for degeneration to occur, and then determining the residual populations in each case. The total neuron populations of a number of structures related directly to the mammillary nuclei are determined also. In addition, the size distribution of the nucleoli of the neurons is measured for each of the structures of interest in the population determinations. The methods and techniques that have been developed to obtain the necessary accuracy in the determination of the cellular populations are described. These include lesion placement, histologic preparation of the tissue, nuclear‐boundary determination, and neuron mapping. The data presented in this paper constitute the type of information upon which a complete quantitative description of the neural circuitry of brain structures can be deduced, as will be demonstrated in subsequent papers.