What is the difference between presume and asume?

Both these Words, assume and presume have similar meanings in one context: to take for granted that something is true without positive proof. But, both these Words have many variants, shades of meaning. One can "assume" (take on) responsibility for something, i.e. The captain assumed command of the squadron in the absence of the Major. Or, How dare you presume to think that I would want you as a lover? Several other nuances for both Words, each slightly, but significantly different. I suggest any of the online sources, such as www.dictionary.com, which will have thesauruses as well.