I received a book that was on my wishlist and I let the site know I received it. The book is listed on my bookshelf and I am instructed that is not visible to anyone but me.  There is also a red W does this mean that the book is on another's wishlish or is this an indication that this was once on my wishlist.  Now I know I have the option to keep my books or send them back into the system.  Knowing if the book was "wished " by another does make me want to potentially share-maybe-my books to me a like my babies. Please advise

Yes, a red W means the book is Wish Listed ... and a green W (with a tiny A) means the first person in line for it has the book on Auto-Request=yes.

Okay so my book is on anothers wishlist and then a green w with a little a means....when I , if I, or if someone puts the same title up on their bookshelf or I  put it back on my bookshelf they will automatically receive it if they have the credits?? Is that what auto request means???

It is auto request.  If you drag your mouse pointer over the W it will tell you if it is WL or WL with auto request turned on.  here is the help doc info and the link to the help document: Posting and Sending WL Books

• If the book is set to auto-request on the a member's Wish List, the book will be requested automatically, and you will get the email notifying you of the request about an hour after you post the book.

• In the meantime (before the hour is up), you will see the auto-requested item ONLY on your bookshelf, with the notation "request pending-1 hr max." next to it.

• However, if the Wisher then cancels this request, you may log in and find no request there!

• You will have received an email notification of the auto-request, but you will NOT have received an email notification of the first Wisher's cancellation because the offer has been passed along automatically to the next Wisher, without generating an auto-email notification. If no one else is wishing for the book, and the first (auto-requestor) cancels, then you WILL receive an email notifying you of the cancellation.