Julian Maslowski
Julian Maslowski voted up HappyTwo BeHereTwo's answer

Won't is "will not."  Wouldn't is "would not." 

The difference is subtle.

Will is more concerned with an inevitable event.  Will not/won't has more of a "no way," connotation. 

Would is more of a condition or mood. 

However, there are occasions were "would" is the past tense of "will."  "He said he would do the dishes."

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