A project in MapTiler Desktop is a work in progress process of turning an image into map tile. Saving and loading projects is available in MapTiler Desktop PRO version.
To save your work, click in the main menu on File -> Save project…. Loading is similar: File -> Open project… or double-click on the saved file in your file browser (make sure MapTiler Desktop is associated with the .mtp files)
The default save format is MapTiler Desktop Project file with .mtp extension. It consists of a set of commands for MapTiler Desktop (and MapTiler Engine). The file can be opened in any text format and particular commands are here visible in a human-readable form. Moreover, it can also be executed by another installation of MapTiler Desktop (or MapTiler Engine). This can be used as an optimization method by selecting parameters and visual georeferencing done in a graphical user interface and rendering on a faster machine with more CPUs without a graphical user interface.
The default shortcut for saving is Ctrl + S (Cmd + S on macOS) and Ctrl + O (Cmd + O on macOS) for opening.