Microsoft Project Server 2010 is built on Microsoft SharePoint Server 2010 so for an administrator of SharePoint farm can play a role of Project Server administrator. I hope that this wiki article would be helpful for a new administrator of Project Server 2010.

First thing, I would suggest downloading the Project Server 2010 Administrator’s guide which is available as a free download.
Here is the link:
http://technet.microsoft.com/en-us/library/gg663916.aspx

Download the Project Server 2010 Product guide:
http://www.microsoft.com/project/en-us/project-server-2010-product-guide.aspx

Andrew Lavinsky [MVP] has written an excellent blog “10 Things SharePoint Admins Should Know About Project Server”

http://azlav.umtblog.com/2011/08/02/10-things-sharepoint-admins-should-know-about-project-server/

There are books available for Project Server 2010 (Written by Dale Howard, Gary L. Chefetz & Tony Zink)
Implementing and Administering Microsoft Project Server 2010
Managing Enterprise Projects Using Microsoft Project Server 2010

There are a lot of videos to learn Project Server 2010:
Video demos and training for Project Server 2010

Other materials