Yes, you can repair holes in sweaters! In fact, that’s exactly what Father Mackenzie was doing when the Beatle’s described him in Eleanor Rigby!
To quote Dictionary.com:
darn·ing:
/ˈdärniNG/
noun
noun: darning
the skill or activity of mending a hole in knitted material by interweaving yarn.
"long hours of tedious darning"
knitted articles being mended or needing to be mended
So, now that you can visualize Father Mackenzie, darning his socks in the night, it’s time to grab that holey sweater.
First off, I’d like to suggest that you wash your sweater on cold, then lay atop your drying rack to dry. This will help ensure that there are no moths or moth eggs in your cherished sweater.
Now that that’s done with, we may begin.
You’ll want to find thread that matches the best you can.
Next you’ll want to grab all the loose loops and gently go horizontal, then vertical, until you repair the hole.
This is a bit hard to explain, so I’ll show you in photos below.
In retrospect, I possibly pulled my thread a little tight and caused the outside to pucker just a bit. The hole was actually fairly large sized, so I think next time I might put a small piece of fusible interlining on the inside to give me something to stitch to.
I was saved by the fact that this is a very busy-printed sweater, so once I zoomed out you don’t even see the hole. At this point, my major concern is to stop the hole from growing any further. Success!