For an introduction in a context other than algebra, there's a nice (to some of us!) section of Steenrod's book on Fiber Bundles, but it has several disadvantages unless you're (approximately) in your first year of a mathematics graduate program: somewhat old-style language and notation, a rather dense writing style (each sentence make take a half-page of your own notes to work out details), and a pecuiliar sense of what makes them interesting --- you won't see anything about dynamics in physics, etc.
Still, I like it a lot, and it was my knowledge from Steenrod that I put to use when I wrote about quaternions for the book Computer Graphics, Principles and Practice, 3rd edition.
BTW, if you can find a turn-of-the-century copy of Maxwell's Treatise on Electricity and Magnetism, you can read the most baffling verbiage imaginable about quaternions, further complicated by Maxwell's use of Fraktur fonts. When you see a sentence that begins something like "The vector part of a vector is distinct from its real part,...", you know you're in for a bumpy ride. On the other hand, encoding the (negative) electric potential as the real part of a quaternion and the electric field as the "imaginary" part, and similarly for the magnetic stuff (although there's not a lot of magnetic "potential" around, I believe) makes Maxwell's four equations become just two, which is kinda fun, if you're a glutton for that kind of punishment.