Historical, but seemingly still current, textbook by Arthur S. Hathaway – a Primer of Quaternions. This text provides students with a fundamental understanding of quaternions. Prerequisites include a ‘thorough knowledge’ of algebra and geometry.

# Free Quaternions Textbooks

Before I started maintaining The Free Textbook List, I had not heard of quaternions. From a brief study of the topic to create this category, it would seem that it is a field that is strongly tied to both mathematics and physics. Since the first textbook I found on this subject was written by a member of that university’s mathematics department, I have followed their lead and included it under mathematics too.

William Rowan Hamilton (1805-1865) was an Irish physicist, astronomer and mathematician. He made numerous contributions to a number of fields but is best known as the inventor of quaternions. He had been looking for ways of extending complex numbers to higher spatial dimensions. He described a quaternion as “an ordered four-element multiple of real numbers, and described the first element as the ‘scalar’ part, and the remaining three as the ‘vector’ part.”

Hamilton’s work is used in both theoretical and applied mathematics. It is often used for calculations involving 3-dimenional rotations. Practical applications include: computer graphics, control theory, signal processing and orbital mechanics.

Hopefully, you can forgive my little attempt at explaining this subject and instead utilize one or more of the free online quaternions textbooks I’ve listed and shared with you.

## List of Free Quaternions Textbooks

### Application of Quaternions

Free online, 39 page textbook on Quaternions written by Gernot Hoggmann. It has been updated and translated several times. Last updated October 2014.

### On quaternions, or on a new system of imaginaries in algebra.

He was an astronomer and mathematician. Sir William Rowan Hamilton is remembered most for his groundbreaking work with quaternions – a concept he invented.