This chapter represents a transition between the theory established in previous chapters and applications of it in philosophy and science. It describes the core thesis of LIR and shows how it can function as a new methodology for talking about specific areas and theories of reality. It begins with a statement of the thesis and the two-level framework for analysis to which it leads, presented as a metatheory, and aspects of intertheoretic relations and part-whole relations are interpreted following the LIR axioms. The second part of the chapter deals with the structure of reality as defined by LIR both ontologically and metaphysically. This is the basis for subsequent analysis of particular philosophical and scientific theories and provides an introduction to discussion of the specific structural realism of LIR. The final Sections position LIR in relation to the on-going philosophical debates about the analytical/synthetic distinction and explanation and their relation to the LIR structuralist conceptions.