I'm looking for a good introductory book/course on Support Vector Machines.
My statistical background is almost non existent, so the more introductory the better.
Hastie et. al.'s "Elements..." is a brilliant book, but might be somewhat hard for first encounter with the subject. Check out their more introductory course http://online.stanford.edu/course/statistical-learning-winter-2014 (week 9) and accompanying book (available for free download). There are also excellent explanatory videos on SVMs in online courses "Machine Learning" by Andrew Ng and "Learning from Data" by Y.Abu-Mostafa.
How about Hastie, Tibshirani and Friedman book: http://statweb.stanford.edu/~tibs/ElemStatLearn/ chapter 12. You need to be able to read and understand mathematical notation though.
Not a book, but some of the explanations on this reddit thread are quite good!
We're looking for long answers that provide some explanation and context. Don't just give a one-line answer; explain why your answer is right, ideally with citations. Answers that don't include explanations may be removed.
Lutz Hamel's Knowledge Discovery with Support vector machines is the most introductory book on SVM that I know of. It builds up very slowly (like: what is a vector) and is completely self-contained. All the mathematics required is very well motivated.
While I second Hastie et al.s ESL. They do assume some statistical background. Like the OP, I had absolutely no background in statistics and that made some parts of the their discussion on SVMs difficult (especially the bit on tying it with some sort of regularized logistic regression).
A much simpler option is James et als. Introduction to Statistical Learning. This is a simplified version of ESL. The best thing about the book, however, is that it is a very good and rapid introduction to R.
I have found the relevant lecture notes in the following MIT-OCW a good launching pad to understanding SVMs: Prediction: Machine Learning and Statistics. Though, unforunately, this too assumes some basic statistical knowledge. It also assumes some mathematics background.