Know - Sure knowledge. Ex: I know the sun will rise tomorrow. Know of - Heard about. Ex: I know of a good Sushi restaurant. I haven't been there but I heard from my friend that it's good. Know about - Knowledge about......something. Ex: I don't know much about auto mechanics but I do know about plants.

Differences: I know Peter- means I have met Peter. I know about Peter - I may not have met him but I have heard (often bad things) about Peter I know of Peter - is neutral or positive meaning you have heard of him but know little or only good things about him. If your car needs repair I can say: "I know of a good mechanic" - which is a recommendation. You can also use 'I know' but not ' I know about a good mechanic' in this sense.