"Potential Theory and Right Processes" is a specialized book that addresses the latest developments in potential theory. It expands the understanding beyond classical excessive functions and introduces the world of strongly supermedian functions. These functions, introduced by J.F. Mertens and studied by various scholars such as P.A. Meyer and G. Mokobodzki, play a central role in modern potential theory. The book aims to develop a suitable potential theory for this new class of functions and combines analytical methods with probabilistic approaches from Markov process theory. It covers the fundamentals of the theory, including Ray topology and compactification, as well as various types of negligible sets in the context of finite mass. The comprehensive analysis and theoretical tools presented in this book are of great interest to professionals and students of mathematics.