I have filled up one of my external hard drives and would like to transfer some of the images to a new hard drive. How do I move some images to the new drive both physically and in Lightroom so that I do not lose all of the Lightroom settings and adjustments? All of my images are in a single catalogue, and I would like to keep it that way, so I can't simply move the catalogue.
You have two options:
(1) move the files outside of Lightroom, then fix up the paths inside Lightroom
(2) move the files inside of Lightroom where Lightroom automatically updates the database with the new locations.
#2 is the easiest if moving one directory at a time:
In the Library module, in the Folders tab on the left, click the "+" and choose "add folder...".
Navigate to the new drive, create a new folder if needed.
Select a bunch of files in the Library grid view, drag and drop them to the new folder in the Folders tab.
If you want to replicate a tree of directories, you might be better off doing the external move (#1), then in the Library module find the old root directory that got moved in the Folders tab, right-click to "find missing folder", navigate to the new location of that directory on the new drive. Lightroom will fix up all the files and directories under the fixed directory.