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Measuring the properties of the Higgs boson is one of the most important missions for remaining runs of the LHC. These measurements can be understood and optimized with intuitive and powerful tools from information geometry. The central object is the Fisher information matrix, which defines the maximum precision with which theory parameters can be measured in a given experiment. In this talk, I will discuss how the Fisher Information can be used to i) improve event selections, ii) determine the most powerful observables, iii) compare the power of multivariate techniques to traditional histogram-based analyses, and iv) analyze the impact of theory uncertainties on Higgs coupling measurement. I will further present a new Python package, MadMiner, that allows to calculate the Fisher Information in the presence of detector effects, using a set of new analysis techniques that combine physics insights, statistical methods, and the power of machine learning.