1. Introduction1.1. Methodology: Framing scientific knowledge 1.2. An Overview of Maxwell’s approach to methodology1.3. Maxwell’s initial publication of 1856 (an abstract)—placing methodology at the forefront1.4. Methodology as an essential feature of scientific practice: The case of Maxwell1.5. The argument2. Maxwell’s choice: Faraday vs. Ampère2.1. Michael Faraday (1791–1867) and James Clerk Maxwell: A unique relation2.2. André-Marie Ampère (1775–1836): The contrast3. Thomson, Stokes, Rankine, and Thomson and Tait3.1. Introduction: Methodology in electromagnetism3.2. William Thomson (1824–1907): From analogy to representation3.3. George Stokes (1819–1903): Idealization3.4. William J. M. Rankine (1820–1872): Energy—a novel unifying concept3.5. William Thomson and Peter Tait (1831–1901): Abstract dynamics3.6. Conclusion4. Station 1 (1856–1858): On Faraday’s lines of force4.1. A novel methodology: Modifying the methodology of analogy4.2. The structure of Maxwell’s argument4.3. From the general to the specific4.4. Confronting Ampère’s theory4.5. Conclusion4.6. Appendix: A bibliographical note on Maxwell 18585. Station 2 (1861–1862): On physical lines of force5.1. Introduction5.2. Preliminary: From instrumentalism to causality5.3. The methodology: Linking hypothesis to representation5.4. Applying the methodology: Assumptions and their consequences5.5. Part III: A landmark in the history of physics5.6. Conclusion6. Station 3 (1865): A dynamical theory of the electromagnetic field6.1. Introduction6.2. Part I: Marking the goal—the construction of a formal theory consisting of a set of general equations6.3. Part II: The flywheel analogy6.4. The methodology of reversing the argument6.5. Intermediate summary6.6. A physical theory in symbolic language6.7. Conclusion7. Station 4 (1873): A treatise on electricity and magnetism7.1. Introduction7.2. Framework7.3. Novel methodologies7.4. The impact of the new methodologies on the construction of the theory7.5. Conclusion8. Philosophical reflections on Maxwell’s methodological odyssey8.1. Commitment 8.2. Modifications of methodologies8.3. Methodologies in Maxwell’s practice8.4. Concluding remarks9. References