The Method of Moments and Its Applications in Plasma Physics: How to Find the Dynamic Properties of Dense Plasmas Using the Sum Rules and Other Exact Relations

What to do if there are no reliable small parameters in a physical system like a moderately or strongly coupled plasma and we have to describe its modes and other dynamic properties? Apply the method of moments! It is a mathematical approach dating back to the works by T. J. Stieltjes and M. G. Krein. We show how it works and describe its new fruitful modification, the method of moments with local constraints. Results of the moment approach application are provided. Destined to Ph. D. students in Statistical and Plasma Physics.