I am currently taking a course in pattern recognition, and several times I have encountered the multivariable normal distribution and thus, Mahalanobis distance. I want to understand Mahalanobis distance; Primarily for understanding the normal distribution, but also to understand the measure itself. I have read several intuitive explanations here and in books, but how can I do this rigorously? I have had some, but not much, measure theory (in the part of a real analysis course that covered integration theory). I have had one introductory statistics and probability theory course. What should I read to understand the Mahalanobis distance? Clearly it is related to ellipoids, but how? Again, I don't want a rough intuitive explanation.