I recently wrote a (very) short introduction to the Sleeping Beauty problem for the website 1000-Word Philosophy (link here). In an age of excellent free online philosophy resources like the Internet Encyclopedia of Philosophy and the Stanford Encyclopedia of Philosophy, 1000-Word Philosophy is unique in that it offers extremely short and novice-accessible introductions to a wide range of philosophical topics. If you haven’t yet checked it out, do so, and if you happen to be a professional philosopher or grad student, considering writing your own entry!
Side note about my Sleeping Beauty article: while I think I do a pretty good job of very quickly laying out a few of the “classic” arguments (insofar as any arguments in a literature that dates back to 2000 count as “classic”), I don’t have space to set up or discuss what I take to be the best paper on the topic, Rachael Briggs’s “Putting a Value on Beauty“. So if you read my article and want to know what I actually think about how we should solve the Sleeping Beauty problem, read that next.