This chapter outlines the theoretical machinery of the framework that shall be assumed throughout this monograph, the so-called <i>Minimalist Program</i> (see Chomsky 1993a and subsequent work). The chapter is divided into two main sections: the fist one considers the specifics of the operations <i>Merge</i> and <i>Agree</i>, its relation to former operations (e.g., Attract, Move), and its role both within the narrow syntactic component and at the interfaces. Building on Chomsky (2007; 2008), it will be argued that labels are not created (in the X-bar sense), but rather identified by a minimal search algorithm; likewise, Merge will be taken to be less feature driven than is usually assumed since Chomsky (1986b; 1993a). The second (and shorter) part delves into the notion of <i>syntactic cycle</i>, providing a brief summary of the main motivation and advantages of this way of conceiving computations. This sets the stage for the second chapter, where a critical and detailed assessment of <i>Phase Theory</i> is carried out.