The need and benefits of new universal mathematical and especially algebraic and operator structures and methods in all branches and levels of modem physics from experiments to fundamentals is nowdays widely recognized. The far reaching pioneering discoveries of R. M. Santilli extend significantly the Lie analysis and operator methods and models of modem physics opening new areas of applications with possible essential improvements and revisions in models in particle physics and cosmology. In this article, some fundamental aspects of Lie-Santilli isotopic theory and relevant references are presented.