Suppose we have two $n$ by $n$ matrices over particular ring. We want to multiply them as fast as possible. According to wikipedia there is an algorithm of Coppersmith and Winograd that can do it in $O(n^{2.376})$ time. I have tried to look at the original paper and it scares me. It seems that it is impossible to understand current state of the art.

So, the question is the following. Is there any 'gentle' introduction or survey for beginners in this particular field? I took only introductory course in algebra, so it would be nice to know what parts of algebra do these techniques rely on.