Is it possible to search the contents of notes?  Thanks.
Yes, on the desktop version. First do a search as you would normally (type in the instant search box and either press Search or hit Enter). 
This should pull up the search tool pane. When the search is finished, click the Advanced button. 
Up at the top, click Clear All and then check only the Notes box. Then click Ok. 

The search results should only show thoughts that contain the term in the notes.

macOS 10.14.6
TheBrain 11.0.119


Yes, Notes are always indexed and searchable. We have a tutorial on Searching available:

Also, if you are new to TheBrain, I'd like to recommend joining us for our Live, TheBrain 101 web event available every Friday at 10:00 am Pacific Time. This free web event is the best way to get started on your Brain. We cover all the basics so you will be able to get going on your own Brain quickly. We also take specific questions so you get a live demo of any aspect of TheBrain that interests you.
If you're interested in joining this event, visit: http://www.thebrain.com/support/101 for more information. If you are not able to attend, we also have a pre-recorded 101 available on the signup page as well.
Outstanding, thank you!

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