I'm talking like when your at school in the library, out to eat, on the bus ect.. Girls always look at me and i take it there interested and want to know who i am but i dont know if its an ok time to approach, pretty much just wanting to know from you guys is if she looks at you shes interested in, should you just go talk to her no matter what your doing, is that what they want

Yes of course they want boys to be interested in them. Think about how much time they put into looking good to attract males. Just be calm. Pretend you aren't hitting on them, even to yourself. Tell yourself you are just making friends. Each girl is different and each approach is different. It's litterally either you are good and you adjust to different situations or your not. How can you plan and script getting a woman? Better to have a basic overall strategy

And no matter how good guys say they are everyone gets regected. You can't even get good without being rejected many many times. You'll see. lol. Stick with it and have fun and keep it fun for the woman

rakeal is right everyone fucks up the approach at some point. its how we all learn. but if i may rakeal i wanna take what you said a step farther. pretend you are talking to your younger sister. make little back handed compliments we in this world call negs. it basically reassures her your not hitting on her. a great example of this is "oh i like you nails are they real?" (most likely the answer is no) "oh...well...they still look nice anyway"
see try this on a couple girls after getting to know them a lil while and see how they react. and when you approach start with a conversation opener. for example "me and my friend were discussing this at lunch today and i just gotta get a woman's opinion. who cheats more men or woman?"
get back on here after your first 10 times of trying these lines or something of your own and tell us the results.

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any man can sweep any woman off her feet. just need the right broom

There is not a bad place to approach a woman, except maybe a funeral or while she's giving birth. If she smiles at you and you're feeling good, take. the. shot.

Guys honestly what is wrong if the girl knows that you are hitting on her? Pretending that you are just making friends, wtf ? Why don't you just be honest to yourself and do what you really want to do instead of making it safe to avoid having to take risks ?
If she looks at you and smiles then she says "Please approach me and hit on me because I think you are cute". So just go and introduce yourself and take it from there.
You can of course make your life difficult by using negs/routines/cold reading and shit like that but I don't see why is that necessary.
And please forget about negs completely. That is not for inexperienced guys and 90% of the time it will come off as an insult.

walking up to a 6 or 7 at best and just doing a regular approach and showing attraction might work but if he is going after 8 and above its gonna be more difficult. from the age of 13 women have been hit on thousands of times from guys using the same old boring shit like can i buy you a drink and you have beautiful eyes. it just doesn't work on hb8 or above anymore. but i do agree that negs can come off as an insult IF you do it incorrectly and IF you do it on the wrong girl. negs are made for hb8 and above so you can lower her value and through dhv spikes raise your own. then i usually like to back up a neg by usunig david's cocky funny. works 90% of the time.

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any man can sweep any woman off her feet. just need the right broom

I think you are talking about club approaches don't you ? Girls in club hit on every time even the not so attractive ones so in the club being direct and honest doesn't work very well I know.
Maybe you are right but from my experience when I approached hot girls they said that it's really rare for a guy to just come up to them and be confident enough to show their intentions from the outset.
OP also mentions that these girls clearly show interest. In which case your job is simply not to screw up.
Maybe it's just me but I like to keep things simple and always be honest and don't follow any routine.

A girl who is a 7 to you could be a 2 to me, and vice versa. It's purely subjective. Whether she's a 1 or a 10, she's still a woman, and still has the same needs as any other girl. It is wrong to say that one girl should be treated differently from another based purely on looks. You only neg if you can tell she thinks she's hot shit, and even in that case, I don't always advise using negs at that point. Most people don't do them right at all. The example you gave in a previous post isn't a neg, by the way. Lastly, the point of a neg is not to lower her value. Why would you want to make someone feel worse about themselves? You should be empowering people. That way, they will associate you with good feelings and will want to spend more time with you.

thats what i always did at afc level and only got the same results. the lets just be friends speech or the your too nice speech. and the neg i mentioned came straight out of mysterys mouth bro. there is no problem being honest with her if it works for you then it works for you. im just saying that the mystery method so far has not let me down

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any man can sweep any woman off her feet. just need the right broom