The Undo and Redo have disappeared from my Word Home ribbon.

You have received good suggestions from Hans and Jay

I'd like to add that you can always use the built-in keyboard shortcuts: Ctrl+Z for Undo and Ctrl+Y for Redo.

The advantage of having Undo and Redo on the Quick Access Toolbar is that there they're always available, even if Word has switched you to another ribbon such as Table Layout or Shape Format. If you really must have them on the Home ribbon, though, there is a way.

Word will refuse to add any commands to a built-in group on any ribbon if they aren't already defined as part of that group. The solution is to add a custom group, and then add the commands to that group.

Go to File > Options > Customize Ribbon. In the list on the right side, click on Home. At the bottom of the list, click the New Group button. Use the up and down arrows in the right margin to move the new group to the position you want, and use the Rename button to change the name of the new group. Finally, while the new group is selected, click the Undo command in the list on the left side and click the Add button. Repeat for the Redo command.

As Hans and Jay have pointed out, the usual location for these buttons is the Quick Access Toolbar. The problem is that apparently you don't have the QAT displayed, but Hans has explained how to fix that. Most of us who have loaded up the QAT with commands prefer to display it below the Ribbon, but above the Ribbon is the default, and I don't see it there in your screen shot.

I virtually always simply use the keyboard shortcuts.

However, when I'm doing extensive editing, the OAT buttons are handy because they show a history and you can go back to a certain point, and then, assuming no new changes, forward again.