Summarize the following:
If a girl who catches your attention, try to quickly make eye contact and smile as you walk past her. Don't stare for too long, and then look away for a few seconds to give her a chance to look you over, if she is also interested. If you glance back and catch her looking at you, smile and give a quick wave. If she smiles or waves back, walk right up to her. Then proceed straight to the third part: Starting the Conversation. If you do not see her looking back, that does not necessarily mean she is not interested. She may not have seen you, or you may have missed her glance. You're going to have to keep at it to find out. If you do catch her looking back, and she quickly turns away from you and walks on, that's a signal that she knows you were trying to connect with her, and is brushing you off. Let this one go. You can either walk quickly to catch up to her, or follow her until she reaches a crosswalk and has to stop. Walk a few blocks if you have to, in order to approach her in a calm and natural fashion. Do not tap her on the back or startle her from behind. This can come across as threatening. It would also be inappropriate and frightening to the woman if you were to run after her, or approach her all sweaty and out of breath. As Han Solo once advised, "fly casual." There is a huge difference between following a person for a few blocks in order to catch up and introduce yourself, and stalking someone. Do not follow the girl for more than two or three blocks, and pay close attention to her signals. If she does not make it easy for you to catch up to her, she is most likely not interested. If the girl seems to be speeding up, making it hard for you to catch up, she is aware of your approach, and trying to shake you off. If she gets out her phone to make a call, this is another strategy for shaking off an unwanted advance. Take it as a hint to back off and leave her alone. Do not try to follow her until she is done with her call, or the next call she makes could be to the police. Don't follow a person into an office building or other place of business. If she casually wanders into a coffee shop or store, you may try approaching her there, but bear in mind that there is a good chance she is alarmed by your approach, and looking for witnesses and/or assistance in getting rid of you.

Summary:
Try to make eye contact as you pass by. Glance back and try to see if she noticed you. Turn back and approach the girl from the side. Do not stalk the girl.