What is the best tool used for project management?

Project Management is a very vast subject which required multi-disciplinary skills and there are many tools available to practice it. The answer could be different for different situation/project based on the specific requirement.  In very basic terms, if we develop structured processes and checklists after having complete knowledge of the project, even a novice team can manage a project in very effective manner.  

My opinion, the best tool is : Analyze the each of ( environment changes, speed of processes, cost of processes)

The best tool for project management for me is accepted the customer request.

The best tool for me is to determine the responsibilities follow up and control of implementation

You can use either Microsoft Project or Primavera.