Looking for a Simple Project Management and Tracking Tool

Hey, I'm running a small construction app and it has expanded to the point that I need a proper tool to manage all our projects instead of excel sheets now.

My basic requirements are just for an admin to create a new project, mention its various parts or phases and deadlines of each phase.

Then the user heading each project can login separately into his project and mark each phase as finished whenever they're finished. And if they're not finished by the ending time assigned by the admin then the admin gets a notification and can issue an extension.

I've a good background in creating web apps in python/PHP, but before I dive into it I wanted to know if some simple open source tools exist which will be able to remove a bulk of my work.

I did take a look at a some open source project management tools online but they're incredibly complex with so many frills I don't need.

I'd appreciate some recommendations...thanks!!