mac the system steps to upgrade or downgrade

Reference material

apple official - How to create a bootable installer macOS

How to restore function by macOS reinstall macOS

MAC cloud classroom - nanny-level course! Teach you how to downgrade back to Mojave MacBook from Catalina system

Change System Considerations

Lifting system, the data will be cleared, note the backup, comes with time machine tool very easy to use, fast speed external hard drive, then so much the better.

Network installation system (three not recommended)

Dependent network speed, resulting in a large mirror mounted very slow

You can not specify the installation system version

Reinstall the latest macOS fitted on your Mac

Command (⌘)-R
Upgrading your Mac to be compatible with the latest macOS.
Option-⌘-R
Reinstall Mac that came with it, or closest to, and still provide a version macOS.
Shift-Option-⌘-R

u disk to install the system

Click for link after xxx, will jump to appstore == == macos in, and follow the instructions to download system
Use "createinstallmedia" command in the "terminal" in
1. It is connected to the guide for a mounter U disk or other volume. Ensure that the drive has at least 12GB available storage space, and has been formatted as "Mac OS Extended" .
2. Open the "Applications" folder in the "Utilities" folder "Terminal."
3. Type or paste one of the following commands in the "terminal" in. These commands assume that the installation is still in your "Applications" folder, and MyVolume is the name of the U disk or other volume that you are using (U recommended to format the disk name change has nothing to do with the name of the system disk name, such as change "aaa", otherwise there may be "Erasing Disk:. 0% ... error erasing disk error number (-69888, 0) a error occurred erasing the disk" error). If this is not the name, accordingly replaced
  
  Replace your volume name.
  
  Catalina
```
sudo /Applications/Install\ macOS\ Catalina.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume
```
  Mojave
```
sudo /Applications/Install\ macOS\ Mojave.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume
```
  High Sierra
```
sudo /Applications/Install\ macOS\ High\ Sierra.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume
```
  Sierra
```
sudo /Applications/Install\ macOS\ Sierra.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume --applicationpath /Applications/Install\ macOS\ Sierra.app
```
  Captain
```
sudo /Applications/Install\ OS\ X\ El\ Capitan.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume --applicationpath /Applications/Install\ OS\ X\ El\ Capitan.app
```
4. After you type the appropriate command, press Return.
5. When prompted, type your administrator password, then press Return again. When you type the password, "terminal" will not show any character.
6. When prompted, type Yto confirm that you want to erase the volume, and then press Return. Create a bootable installer process, "terminal" is displayed progress.
7. When the same "terminal" show this operation has been completed, the name of the volume of the downloaded installer with your name, such as "install macOS Mojave". You can now exit the "terminal" and the pop-up volume.
* If your Mac is running macOS Sierra or earlier, use the --applicationpathparameters, the specific manner in order to use this argument applies to the Sierra and El Capitan is similar.
Restart the computer, before the screen by the lights command+R, in the recovery mode, using a boot security tools in utility, security, and without selection to allow external boot media
Computer shutdown, u disk is inserted, the boot according to optionnot loose, selecting u disk system, comes after entering the recovery mode, the original built-in type hard disk formatted == == (there format selected, depending What type of partition you want to install the required version of the system), then after returning to the installation system, you can click next be installed according to instructions.

Note: I installed the system encountered a problem u disk production failure. Is stuck in the process of copying installer files to disk, the most thought it was u disk broken, in fact, u disk write speed (usb2.0) caused by too slow, a wait 10-15 minutes just fine .

Early adopters will try to upgrade the system, but sometimes out of the new system stability almost always, after the early adopters, can not stand the large and small bug, the pursuit of stability of students (like me) or a downgrade to the old system, look at the individual the choice.

Finally, I wish you a pleasant upgrade and downgrade system.