This is a combination of the default mod_menu and mod_login modules.

Requires the Bootstrap framefork or its nav, nav-pills styles.
The mod_menu integration allows to select site menu which will be displayed in the module.
The mod_login module gives an option of login/logout redirect menu items.

Usage:

1. Download the .zip from the releases section of the repository.
2. Go to the Extensions -> Extension Manager in the admin Joomla part.
3. Drag the zip onto the upload field and Upload & Install.
4. Go to the Extensions -> Module Manager -> Site.
5. Click on the Menu With Login.
6. Select the Navigation position for your site theme.
7. Select Published in Status.
8. Select On all pages in the Menu Assignment -> Module Assignment block.
9. Press Save.
10. The menu should appear on the main site below the page title.