I must have first heard of the law of large numbers as an undergrad, but I remember later in a more advanced course learning properties of estimators, unbiasedness, efficiency, and consistency etc. I never made the connection, but isn't the LLN basically just a statement that the sample mean is a *consistent* estimator of the population mean?

Also, I doubt it makes the list for being a fundamental theorem, but in graduate school the series of 'slutsky' theorems presented in Goldberger's 'A Course in Econometrics' were pretty interesting tools.