In this article, you can find what permissions are required to execute the different steps of an Email Marketing Campaign. 

Permissions for creating a Campaign

To create a campaign or modify an existing one, you will need the following permissions under:

Setup > Campaign

Permissions required for Audience Management

To create and manage Audience Profiles, you need the following permissions under:

Audience > Audience Profile

Also to create and manage audience segments, you need permissions under:

Setup > Data Management Platform

Permissions to Create an Email Marketing Content Template

To manage your Email Marketing Content Templates, you will require following permissions under:

Setup > Content Templates

Publishing Permissions

To create or edit an Email message and publish it through Advanced Publisher or the Quick Publisher, you will require the following permissions under:

Publishing > Outbound Execution