Design Manager is a new feature introduced in SharePoint Server 2013 publishing sites to manage branding. You are not seeing "Design Manager" in SharePoint 2013?
Well, to enable design manager in SharePoint 2013, You got to activate "Publishing" Feature!
- Go to "Site Settings" of your root site collection >> Click on "Site collection features" under site collection administration
- Click on "Activate" button next to "SharePoint Server Publishing Infrastructure".
- Activate "SharePoint Server Publishing Infrastructure" from site features via "Site Setting" >> Click on "Manage site features" and activate SharePoint Server Publishing Infrastructure.
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