During A2 phase(female-to-male attraction), why do we need to show lack of interest in the target? Does lack of interest mean that you don't want to get her?

Well obviously we do want to get her, but we can't really show it. As you mention A2, you are obviously studying mystery method, which is indirect game. In direct game you do show interest first, however that is a whole different ball game, and has it's own rules and guidelines. Personally I don't like the direct approach (different approaches work for different people).

So...

If we go in on our approach conveying interest we will trigger protection shields. Say your'e at a club and you see a hot girl you want to approach. Chances are, there have been about 10 guys before you who have approached her telling her she's hot, or offering to buy her a drink etc. If you go up and do the same, you'll just be like everyone of those lovable losers. She'll know that the whole interaction that takes place is just about you trying to win her over.

Also it has to do with frame. By indicating your interest first, you're putting her in the position of power - she is the prize, which will make it so much easier for her to tool you.

So going in and not showing interest, her protection shields are not triggered. The interaction is not about you trying to win her over, you're just some guy who's sociable, talking to her whole group, without an agenda. Then, when she is attracted to you (you detect clear ioi's) you can then convey interest to her (A3). However, even in A3 you can't then just compliment her on her looks. You have to qualify her, make her tell you something about her self which you can reward her for by giving ioi's. This will tell her that your not just interested in her for her looks (which she gets all the time). Although remember in A3 to use the bait, hook, reel, release method, which i'm sure you can find somewhere.

So in summary, the whole interaction looks like this - You approach the whole group - you're just a sociable guy just in a chatty mood. The whole group accepts you as you do not pose a threat. You build attraction from the target, then you talk to the target and get to know her, then you show interest. So rather than being just another guy that walks up to her salivating, you are just a cool guy she met at the club and found a connection with.

This is how I do it, based on the mystery method. However there are many different methods, but really the fundamentals are similar.

Thanks for your explanation very much.
What are the essential points of mystery method? What are the threads that run through the whole book?
I proposes two threads:
1.Treat the target as if she was a man whom I want to get to know
2. Always think about how many other guy treats her, and I need to be different from many other guys.
What are your thoughts?

Your explanation is very good. So in one word, during A2 phase, you demonstrate high values and let her realize that you are the prize, right?

During A2, you neg the target and DHV the obstacles. This has two effects: she puts her guard down, and secondly, she's gonna wonder why you're not trying to impress her. Assuming you're gaming the best looking girl in the group, she's probably used to guys hitting on her and giving her all this attention, so by ignoring her you have the upper hand. This creates attraction and she'll try to gain it by trying to talk to you. When she does something you like (buys you a drink), then you reward her with IOIs, and once she's shown enough interest, pull her and isolate her