The three branches of the federal government are the legislature (Congress), the executive (President), and judiciary (Supreme Court).
States also have three branches of government: legislatures (called "state legislatures," "General Assembly," "General Court," or "Legislative Assembly"), executives (called governors) and courts.
Local government branches consist of mayors, councils, select board, or other governing bodies elected by the people. State and local government is explored more fully in Topic 6 of this book.