Alone in class

I'm in the library for history because I wont  have a proper teacher until after summer, but I always sit by myself while the rest of the class (It's not huge as it an advanced senior class in a small school) sit together and talk and joke through the lesson. They all seem nice but I'm not in the friend-group so I don't know how to approach or join in.

I can't even focus on the work because like I said- no teacher- and I keep accidental lightening to their conversations instead of reading the textbook.

I wish I could join in and I feel bad about being quiet and awkward because I don't want to seem cringe and shy, I want them to like me. But that fear is in my head and making me all quiet and awkward so it's a viscous loop I don't know how to get out of.

If only I was social enough to come up with something to say that might begin a conversation natural enough that I can use it as a reason to sit with them, then it would be easier to speak as I wouldn't have the worry that I seem eaves-droppy.

God I feel like a piece of sh*t.