Thank you. Yes, of course I see that in the line at the top of my page. I click on "connect", the mouse works, I use if for a while and it disconnects. On and on this goes. I click on "shift option" in their "advanced" selection and an 'X' appears next to either the "bluetooth mouse" or the "bluetooth keyboard". I clicked on deleting the "bluetooth mouse". Rebooted my computer, waited for the "bluetooth mouse" to come back - YAY!! it did. It worked for a little while, then "disconnected" again. I reconnected (with another mouse that I have to use when the apple mouse isn't working) and it reconnects... for a little while.
There is a "bug" in the High Sierra OS system and there is a way to "debug" it. Here is website that shows you how to do it.
OS X’s Hidden Bluetooth Debug Menu: Reset Devices and More – The Mac Observer
I haven't tried yet... I'm too tired tonight and I have more work to do anyway.
Goodnight and thank you all for your help.