The modules, Categories, target, Link Relationship (XFN), and Advanced, can be expanded, or collapsed, by clicking on the module title bar.
In addition, those same four modules can be moved by hovering the mouse cursor over the module title bar, when the mouse cursor changes to 4-arrows, hold the left-mouse button down, drag the module to where you want to place it, then release the mouse button (this is called drag-and-drop).
Check the box for each module you want displayed, or uncheck the box to not display that module.
Click the Screen Options tab again to close the Screen Options.
If you would like to restore the Links panel to your install you may download and install the Links Manager plugin.