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Brain Connectomics is generating an ever-increasing deluge of data, which challenges us to develop new methods for analyzing and extracting new insights from these data. Connectomic researchers have focused on connectivity -- the pattern of connectivity between neurons. The strengths of synapses have also been studied by quantifying the sizes of synapses which can be regulated by learning. During my PhD, I have been developing computational methods for relating brain structure to function. I have developed tools and algorithms for analyzing connectomics data sets using Machine learning, statistical inference and Information Theory to find measures and biomarkers that can be used to probe mechanisms underlying leaning and memory in normal and diseased brains. We introduce here a powerful method for analyzing three-dimensional reconstruction from serial section electron microscopy (3DEM) to measure synaptic information storage capacity (SISC) and apply it to data following in vivo long-term potentiation (LTP). Quantifying precision is fundamental to understanding information storage and retrieval in neural circuits. We quantify this precision with Shannon information theory, which is a more reliable estimate than prior analyses based on signal detection theory. Spine head volumes are well correlated with other measures of synaptic weight, thus SISC can be determined by identifying the non-overlapping clusters of dendritic spine head volumes to determine the number of distinguishable synaptic weights. SISC analysis of spine head volumes in the stratum radiatum of hippocampal area CA1 revealed 24 distinguishable states (4.1 bits). In contrast, spine head volumes in the middle molecular layer of control dentate gyrus occupied only 5 distinguishable states (2 bits). Thus, synapses in different hippocampal regions had significantly different SISCs. Moreover, these were not fixed properties but increased by 30 min following induction of LTP in the dentate gyrus to occupy 10