Managing Projects is at the heart of administration, some of the capability is available to the project level administrator (the person with Modify permissions on the project) and some aspects are retained by users with admin rights as follows

Modify rights with Team licence

These users can manage the Project Summary information form to set up local reporting aspects of the project, manage permisisons on the project including creating new permissions groups. They can also create and save Project Views and allocate project roles

Modify rights with a Manager licence

These users can also personalise the structure of the projects adding and removing documents etc and produce reports for the Project and save project specific report formats.  These users can also add stages to existing projects.

Manager licence users with Admin

These users can create new projects, delete projects or rename them.  They can also see a full project list so they can also give themselves rights to a project even if they were not invited by the PM.