saving edits

I would like to know how I can edit an image, save the edited image, and re-edit it at another time. Now, if I edit an image and then delete it from the library (not the disk) then re-import it , all the edits are gone. 

By @Reid356642269dqs

Lightroom is a non-destructive editor. It does not change the pixels of the images, but saves the edits as instructions in the catalog. Deleting the images from the library deletes the edits, so don't do that. You can continue to edit the images at any time, and do not have to save edits in the meantime. Edits are automatically saved in the catalog. If you mean you want to make completely different edits without removing the current ones (for example because you want to have a color version and a B&W version), then you use a virtual copy. A virtual copy is a 'copy' that only exists in the catalog, not on disk, because it is only an extra set of those non-destructive edits. If you want to save the images with its edits for use outside of Lightroom, for example because you want to put it on the web, then you must export a copy.

Virtual copies, as per GoldingD's response, or snapshots.

But, I'm not sure that's what you meant.

>> Now, if I edit an image and then delete it from the library (not the disk) then re-import it , all the edits are gone. 

LR holds all edits in the Library database. Deleting an image from the library deletes all edits and metadata changes from the library database. You can explicitly 'save' those edits as an XMP sidecar file (cntl/cmd-S, or you can have this happen automatically but that comes with the performance impact of a lot of disk writing) that is written to the disk same folder as the image and has the same name with a ".xmp" extension.

If you have an XMP sidecar file with an image, then you can synchronise (menu option) the images's folder to reload the image and any metadata and edits in the XMP file back into the LIbrary. This is the way to deal with accidentally deleting an image from the Library.

If you delete from the disk, you'll need to put the image and XMP back into a folder then synchronise.

Virtual copys