Thanks for reaching out. I'd recommend exploring the video tutorials available on Adobe Illustrator support page. These tutorials would help you understand how the different tools within the app work. Hope it helps.
1) If you haven't done so already, select the two circles forming the ring and go to Object > Compound Path > Make.
2) Select all the paths.
3) In the Pathfinder panel (Window > Pathfinder), hold down the Opt/Alt key and click the Unite button (top left) to create a Compound Shape.
You can apply any fill or stroke you like, or none, and can still select any of the individual paths with the Direct Selection tool of the Group Selection tool or through the Layers panel, should you wish to edit them.
There are other ways to accomplish this, but this is the least complicated that comes to mind at the moment.