How do I keep grass on my side of yard?

Gravel would work. Dig down below the grass level along the fence. Lay down some landscape fabric and gravel on top. Another option is to lay down some patio blocks or landscape blocks along the fence after digging out. Gravel is loose and can spread out.

Fred really? Why does this bother you so much that you are willing to take such drastic actions? Not only will it not be eye appealing but you could kill your grass. Do you have a weed eater? You can walk along the fence and take care of it that way. Looks great and not so rough on you.

I wish the only thing that grew thru my fence was grass..... I hate the blackberries, raspberries, ivy and any vines like clematis, honeysuckle etc that I spend all summer pruning off.

Hi Fred, you could put a strip of garden edging down the fence line

https://www.youtube.com/watch?v=tUA2bxC1LTI

or you could run a line of pavers along that line, both of these ideas are no maintenance

Yep a strip of garden edging covered with pea gravel or mulch would work.