so anyway...

well, there's this girl, we'll call her M.
okay first, she liked for about 3 months *& when I get enough courage to ask her out to banquet, which her assured they though she would say yes, she said no & went wwith this other guy, & back to me for a "back up", all after the banquet. i was mad at her all summer, but we still talked. Now, i think she likes me again & we've been talking a lot lately.
should I ask her out, or just keep talking & see what happens

Soudns dangerous; you feel stronger towards her than she does towards you clearly... I would avoid her since it seems like she is just using you as a "backup" an stringing you along, which noone deserves to be put through. You want a girl who only wants to be with you, not someone who only likes you as a 2nd place guy...