Keep Coding

I have taken a series of notes in a book that I read on Google Play books. Is there a way to export these notes all together as a text document or some similar format?

It isn't perfect but here is one way to do it. After doing this you will receive a zip file with your book(s) and an HTML (or JSON) file with your notes.
Follow this link to the Google Data Tools https://www.google.com/settings/takeout/downloads
Click the Create New Archive button
Click the Select None button
Go down to Google Play Books and flick the switch on
Hit the down arrow
Either download all or click on the Select Books radio (a popup will appear where you can select none again and search at the top)
After you have chosen your books, go to Next at the bottom
Pick your export options and you're good to go.

Google has changed this and now if you have Android device you can get your notes on Google Drive. Simply do this:
Open Play Books on your Android device
Go to Settings
Save notes, highlights and bookmarks in Google Drive - turn this ON
This feature is still not perfect. The biggest problem I have is that page number is not recorded properly for most books. Instead, you just have link that opens the page in Google Play Books. Meaning, it'll probably work for you personally, but sharing notes and making sense of notes on different devices is problematic.

there is no such available function at the moment. I have submitted a request already, let's see what google developers say.

It works on some books and not others apparently. I can't produce a summary/review of Guttag's book for my class.I have the print version and just bought the Playbook version.