University of Rome "La Sapienza", Dipartimento di Fisica, Corso di Fisica Teorico (Ruffini)
A brief overview of the foundations of the mathematical Lifshitz perturbation analysis, followed by the definition of the Lie derivative and gauge transformations of the metric, with a discussion of the available gauge freedom in the perturbed metric and fluid variables. Harmonic analysis is developed using Cartesian tensors, and the tensor harmonics and their covariant derivatives are introduced and calculated, together with the Ricci identities needed for their manipulation. THe Lie derivative pages have been used repeatedly in later notes.