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There are 5 project management processes:
Refer also to the Knowledge Area Process map.    Knowledge Area Process Map
According to the PMBOK, Initiating acknowledges the beginning of a project or a project phase. During initiation, the Project Manager is assigned. The Project Manager receives authorization to begin the project. And the Project Manager receives approval to commit resources to work on the project.
From Wikipedia, "After the initiation stage, the project is planned to an appropriate level of detail. The main purpose is to plan time, cost and resources adequately to estimate the work needed and to effectively manage risk during project execution. As with the Initiation process group, a failure to adequately plan greatly reduces the project's chances of successfully accomplishing its goals.
According to the PMBOK, the executing refers to processes performed to complete the work defined in the Project Management Plan to accomplish the project’s objectives in the Project Scope Statement.
From Wikipedia, "Monitoring and controlling consists of processes performed to observe project execution so that potential problems can be identified in a timely manner and corrective action can be taken, when necessary, to control the execution of the project. The key benefit is that project performance is observed and measured regularly to identify variances from the project management plan."
Closing is the formal acceptance and ending of the project.