CONTENTS -- The Essence of Millennial Reflections on International Studies: Methodology -- Methodology -- Formal Methods in International Relations -- Cumulation, Synthesis, and Research Design for the Post-Fourth Wave -- Accomplishments and Limitations of a Game-Theoretic Approach to International Relations -- Game Theory in Practice: Problems and Prospects in Applying It to International Relations -- Reflections on Quantitative International Politics -- Reflections on Millennia, Old and New: The Evolutionand Role of Quantitative Approaches to the Study of International Politics -- Quantitative International Politics and Its Critics: Then and Now -- Qualitative Methods in International Relations -- Case Study Methodology in International Studies: From Storytelling to Hypothesis Testing -- Contributors.