What's the point of a Scrum master when you can have a Project manager?
There is no PM in Scrum — let's start there :) The Scrum team is composed of three key elements: Product Owner (PO), Scrum Master (SM) and the development team. You might have a Tech Lead, who provides tech guidance to developers, but it's also a variation of Scrum. We should keep in mind that Agile favors self-managed teams (see the 10 principles of agility).
Managers can be involved and often are, but their responsibilities and level of influence are different from the classic managers we see in most companies.
How might a manager be involved in Scrum?
The Product Owner and Scrum Master together have enough power to manage a team, which has some managing power itself. But Scrum doesn't have strict boundaries: if your organization has a lot of developers, too many processes that are hard to handle and you see that you will benefit from having a manager — then hire a manager. But be careful about responsibilities and authority you're giving to that person.
«I prefer to think of the project manager as an assistant to the Scrum teams. In this role, the project manager is expected to have the whole-system perspective and to work diligently with each of the clusters or individual teams to ensure that everyone has the appropriate understanding of what cross-team coordination is required — but the teams still own the coordination.» — Kenneth S. Rubin «Essential Scrum: a Practical Guide to the Most Popular Agile Process»
What are the responsibilities of the Scrum Master?
The Scrum Master is the agile coach for both the development team and the Product Owner. He or she removes impediments that the team faces during development and acts as a servant leader plus interference shield. As a servant leader, the Scrum Master doesn't think the team owes him the work done, but instead, he has to help the team make it done. Important: Scrum Master does not have hiring and firing authority, also no command-and-control management power.
What should the Scrum Master know?
Should each team have a Scrum master?
No, one Scrum master can perfectly handle several teams. The number of teams depends on their size and experience in Scrum: an experienced Scrum team might not need that much attention from the Scrum Master as the team that used the traditional waterfall approach in the past.
Is it possible to leave your team without a Scrum master?
Yes, but then a manager should perform Scrum Master's functions and know how to act in a "Scrum way" — rather teach and motivate than command or control.