In Schoology the blue bar has places where you can check your Notifications and Messages. In the upper right corner next to your profile.

Check your Schoology Messages

Anywhere in Schoology you can click on the Envelope Icon (Upper Right) and click on the first message displayed to take you to your messages area.
Note: You will have the number of unread messages displayed next to the envelope icon. It is important to remember that replying to a Schoology message via your email does not count as “viewing” it in Schoology.

Check your Schoology Notifications

Anywhere in Schoology you can click on the Bell Icon (Upper Right) and see the things that Instructors have been doing in your courses (Posting Updates, Replying to Discussions etc…)
Note: You can click on the Hyperlinks to go directly to what the Notification is for.