As of a few hours ago, all I know about quandles was that they had something to do with knots. Since in our modern connected age ignorance lasts only as long as you want it to, I decided to find out more. I found this slide deck by Bob McGrail explains both the definition of quandle and the motivation in knot theory in a measly six slides. (The rest of the talk is how to efficiently compute quandles.)
Sam Nelson has a nice introduction to the general area of universal-algebraic invariants from the Notices, called Revolution in Knot Theory. Nelson also discusses the emergence of virtual knots.
I learned about quandles from Louis H. Kauffman’s book “On Knots”, which is a very unusual and eccentric book, well worth reading, or at least browsing. It is full of all sorts of stuff, mostly about knots.
Kauffman’s web page at http://homepages.math.uic.edu/~kauffman/ has a lot of other interesting-looking stuff.
I was going to mention that it is available online for free, but then I couldn’t find it. But here it is: http://homepages.math.uic.edu/~kauffman/KNOTS.pdf
Sorry, that isn’t it.
Mark, have you seen Lou’s book Knots and Physics? If you think On Knots is good, you ain’t seen nothing yet!
It always makes me sad when a book stops being online for free. I have a bunch of book pdfs saved that I’ll probably never read, just in case…
I took a look at that Knots and Physics book. It looks amazing.