For a quick overview of some machine learning fundamentals, you could check out Hilary Mason's "An Introduction to Machine Learning with Web Data" (http://shop.oreilly.com/product/0636920017493.do) videos. They cover classification & clustering, with theory and a quick intro to some relevant Python libraries.

For your purposes, one potential use could be combing through lots of financial data for transactions that look unusual. (Another very common use for classification is spam filtering.)