What is the difference between independent and mutually-exclusive events?

Conceptually, mutually exclusive events imply that their intersection is the empty set, i.e., they do not intersect. This means that if one event happens, then the other event/events do not happen (only one event can occur).
Independent events refer to events which are not correlated, i.e., the occurance of one event has no influence on the outcome of the other event/events. Let A=event 1, and B=event 2. If A and B are independent, then P(A|B)=P(A). But in general P(A|B)=P(A n B) / P(B).
So P(A)=P(A n B) / P(B), which means that P(A n B)= P(A) x P(B)