Cutting points from a plane

Hey everyone,

I am extremely new to blender, (I used to be able to find my way around, but haven’t used it in about 6 months). I am trying to create a simple logo, but am struggling. I have a plane in the .blend file that I want to cut some points from. I want to make the edges curved, but haven’t found a way to yet. Attached is a picture of what I mean. The place where the chunks of vertices are taken out, I want that to be smooth. I hope that I am trying to convey what I want. (My computer crashed last week, so all the photo editing software I would have used is gone). I know that there is a tool or something to do this, but I’m not sure what to do.

Any help is appreciated.