This article examines the mathematical works of William Rowan Hamilton that led him to characterize certain mathematical objects named Quaternions, in the years between 1843 and 1866. Many expectations about practical applications of the Quaternions were posed, specially the challenge of synthesize the representation of scalar and vector magnitudes; howewer, few years later, these expectations were frustated, and new kinds of powerful instruments came out in mathematical scene, like tensors, for instance. Hamilton's researches, nevertheless, contributed vividly to Algebra's development, underlining the meaning of several algebrical themes. There is another reason to read Hamilton's works in their original form: exploring life and death of the Quaternions, the importance of History of Science becomes evident, in order to instruct and guide pedagogical actions, specially in mathematical and physical themes.