<human>: Greetings again,

Recently, I have been troubled. I am a college student living on campus, and on a regular basis, I eat in one of the campus cafeterias. Over the past few weeks, on Tuesdays and Thursdays, when I go to eat lunch at the cafeteria after my first class in the morning, I have often seen this girl eating lunch at the same time as me. 

The first time I saw her, I was in the midst of a conversation at a table with two of my friends, and I was struck dumb. 

Last Tuesday, I finally worked up the courage to talk to her and introduce myself. This was made more difficult by the fact that she is always sitting with a group of friends. The conversation was pleasant, and she didn't seem at all bothered or uncomfortable.

Then, last Thursday, I ran into her there again, and we talked again. Once again, it was pleasant and friendly, and she seemed smiling and at relative ease, though I was frankly pretty terrified on the inside.

How do I proceed from here? I really like her, but I'm afraid of coming on too strongly and scaring her away. Any help would be greatly appreciated.

Can you give me the gist of the text in a nutshell?
<bot>: I met a girl and am smitten with her. We've only talked twice. How do I go about approaching her from here?