Mac Re-install the OS
External
Internal
Re-install with Data Deletion
High Sierra, El Capitan: Command ⌘ + R while restarting.
Catalina, Other: Command ⌘ + Option ⌥ + R while restarting. If that leads to a wireless network setup and a "spinning globe" that doesn't end, try Command ⌘ + R.
OS X Utilities -> Disk Utility
Reinstalling without explicit deletion of the partition will upgrade and preserve the data.
First delete the partition from Disk Utilities.
macOS Utilities → Disk Utility → Select Internal → <Partition Name> from the left tab. Usually the partition is named "Macintosh HD".
The partition may not be mounted, and it should be mounted with the "Mount" Disk Utility option.
Erase → Specify the new name and the format: APFS (Case-insensitive, Encrypted). It is OK to leave the name as it is "Macintosh HD", this will be also the name of the new partition → Erase. The process should end with a message similar to "Erasing "<Old Partition Name> and creating "<New Partition Name>" → Done.
Leave the partition mounted, otherwise the Install OS utility won't find any disk to install on.
Then go back to macOS Utilities and install.
Adding a new volume to the container
Apple File System (APFS) is preferable, as it's the newest and optimized for SSDs.
Select the container disk or "APPLE SSD ... MEDIA".
Add a new volume with the + icon.
Name
APFS Case Insensitive
⚠️ It is important to choose "case insensitive", applications may have problems running on a case sensitive filesystem (Microsoft Word).
Installation
Then go back to OS X Utilities -> Reinstall OS X.
The computer must be connected to the Internet (wire or wireless): Utilities -> Network Utility.
If I get "The recovery server could not be contacted", it is probably because the time is out of sync, so go to Utilities -> Terminal and
ntpdate -u time.apple.com
"Reinstall OS X".
Select the drive -> Install.