I know this can be hard to do via photos but I was hoping for some help identifying this fabric. It appears to be woven. I’m also interested in suggestions on how I could repair a small hole in it. The pictures, in order, are the outside of the fabric, the inside and the hole. Thanks for the help.
The fabric looks like damask - but I'm not sure what the fiber is. It could be any number of fibers - cotton, linen, silk, rayon. How does it feel and does it have a scent or is there someplace (other than the hole) that you could snip it for a burn test? I have no idea how to repair the hole. Hopefully someone here can help you!
It is a damask in a satin weave. As Linn says, it's hard to identify the fibre content without a burn test. The shinyness suggests silk, rayon or polyester, rather than cotton or linen. Repair options depend what you are trying to achieve. How skilled are you with a needle? A completely invisible repair is a specialist job, it involves taken strands of the same fabric taken from elsewhere, eg inside a seam, and reweaving over the hole. I have tried this myself, but with thicker easier fabrics like wool tweed. If you want make it less obvious and stablise it, you could darn it with a matching thread. It will still be visible, and the results will depend on your darning skills. I don't have a sense of scale in your photos, but it looks like a small hole, too small to suggest it needs patching. I am forever recommending this book, Mend It: The Complete Guide to Clothes Repair https://amzn.to/31GmFsM (paid link) But no doubt there's lots of information on darning, etc, available online.
I was going to suggest taking it to an invisible weaver but that could be pretty costly. Hopefully, since the hole is tiny you can fix it yourself. I agree with Ruth that the sheen on the fabric suggests silk but cotton sateen damask can also have a sheen so the best thing to do is to test it if you want to know the fiber. Best of luck!