This book is about means, not about ends. Our principal goal is to gain insight into the practice of science by focusing on scientific methodology as applied by scientists. We take scientific methodology to convey modes of research, for it combines procedures of thought and action cast into argumentative structures intended to convince the reader of the validity of the resulting claims to knowledge. We examine the generation of scientific knowledge from the perspective of the scientist, not from that of the philosopher. Nevertheless, as historians and philosophers of science we still appeal to the analytical tools applied by philosophers of science with a view to uncovering the processes by which scientific knowledge is generated. We therefore draw a sharp distinction between “method” and “methodology.” As a preliminary, we analyze J. C. Maxwell’s initial publication of 1856 in electromagnetism and outline the overall argument of the book. Maxwell’s contributions to electromagnetism are very useful because he moved from one methodology to another while staying on course toward a single goal. Our study of this case in the history of physics reveals the pivotal role of methodology in advancing scientific research. Maxwell’s methodological odyssey shows that the same scientific problem can be approached from different perspectives, based on different metaphysical assumptions resulting in different procedures of research, that is different methodologies. What makes the case of Maxwell intriguing is that this is a one-man show in which a variety of approaches were taken with a view to generating new physical knowledge.