The object of this course is a certain style or method of doing philosophy known as ``analysis'' that is practiced by "analytic philosophers.'' Our objective is to shed light on what philosophical analysis is supposed to be and how it is supposed to be practiced. As a crude first approximation, it is often said that the analytic tradition distinguishes itself by its emphasis on argumentative clarity and precision, virtues that are meant to be realized by exploiting the formal tools of logic. But in this sense it is clear that philosophy has been analytic, at least in part, since the time of Aristotle. Yet, the emergence of this tradition as distinct from other philosophical practices is normally associated with the works of Frege, Russell, and other early 20th century sympathizers. This being said, if being a practitioner of analytic philosophy is described purely in terms of `tradition', then it is tempting to regard it as nothing more than an excuse for not reading Hegel, Heidegger, Foucault, and their acolytes. Given that, the first purpose of this course is to better understand the sense in which a distinct tradition of philosophical, conceptual analysis emerged around the time of Frege. The second purpose will be to examine how this initial conception of philosophy transformed itself over the course of the last 150 years, i.e., how the method of analysis has evolved. Thus, after examining influential works of the first wave, we will tackle the first profound transformation, which comes with the flourishing of logical empiricism in the 1920s. Our attention will then turn to the first significant challenge coming from within. Due primarily to Quine's works, but more generally inspired by a certain naturalism and pragmatism, the critique of philosophy as conceptual analysis gained momentum, and we will focus on the critique of the logical concepts of analyticity, reference, and modality. The last part of the course will attempt to clarify the different senses in which the analytic tradition continued to develop in the second half of the twentieth century by focusing on important technical and methodological developments in philosophical logic and philosophy of language.