Well, lately I've been looking for a book on quaternions but I've realized that quaternions are a particular case of the named Algebras(I think Geometric Algebra). Since here, I've found all kind of algebra you can imagine, Geometric Algebra, Lie Algebra, Clifford Algebra, conmutative and no conmutative algebra... I am very confused. How can i get into quaternions? Do I have to study only geometric algebra or another one? I think all algebras are quite related between them.
What books would you recommend?
The reason why I am triying to study Quaternions it's because I am studing the Maxwell's book "A treatise on electricity and magnetism" and it is written in quaternions.
Thanks a lot.
The quaternions are a very specific object like the real numbers. There is no reason to plow into entire disciplines to 'understand' them. You can learn all their important properties from the quaternions wiki page.
IMO, despite previous recommendations above to the contrary, think it is a pretty terrible idea to try to use the literature of that time to learn about quaternions. Even reviewers at that time thought Maxwell's treatise was poorly written, and I know from personal experience how ideosyncratic Hamilton and Grassman's works were.
There is simply no reason not to take advantage of the massive clarifications in exposition of mathematics that have happened in the intervening century to learn about quaternions, and then (if you are really bent on doing it) seeing how it as used in the old literature.
Anyone interested in quaternions and physics should also read Lambek's If hamilton had prevailed: quaternions in physics for an infinitely clearer overview.