Windows 10 App Removal and Restoration

Windows 10, like Windows 8 before it, comes with a bunch of useful apps, and it also comes with undesirable apps. Based on work from Thomas Vanhoutte, here is how to uninstall and reinstall them.
First, open up PowerShell with admin rights (right click on the start menu icon).

Get an official package name

If you want to uninstall calculator, but aren’t sure of the official app name, use this:
Get-AppxPackage *appname*

Uninstall an app

If you want to uninstall something, use this:
Get-AppxPackage *appname* | Remove-AppxPackage

Restore all default apps

If you want to reinstall a default app that you deleted, use this:
Get-AppXPackage | Foreach {Add-AppxPackage -DisableDevelopmentMode -Register "$($_.InstallLocation)\AppXManifest.xml"}
Note that this probably results in an English app and may not restore the app you want.

Reinstalling specific apps

If you want to reinstall a default app that you deleted, you might try this:
Get-AppXPackage *appname* | Add-AppxPackage
Learn more about Add functions at TechNet. You might also be interested in how to use Fiddler to manually install apps (designed for Windows 8, for example).