Solution manual and copyright? Recently, I have worked out a solution manual for a book. 

I have not found on the Internet any existing complete solution manual for this book.

Since the solution manual of mine contains every exercise given in the book,
my question is: In order to publish or distribute publicly this manual, do I have to first request the consent of the publisher of the book?

[Editors note: A solution manual is an accompaniment to a textbook that provides the answers and/or techniques to solve the exercises given in said textbook. Other names for these include: answers keys and teacher's handbook.]
I am not a lawyer.

You should talk to a copyright lawyer before getting into contact with the publisher, as the lawyer may be able to provide additional insight. Having someone who knows the ins and outs on your side helps in such a case, and will protect you from any issues that may arise.

As it stands, this does seem like a copyright issue, and you definitely need to talk to someone on the publisher's side before you do any publishing or distribution on your own.

The material is originally the publisher's, and there's probably legalese already included in the book that indicates the content may not be reproduced in any form without permission.

I'm sure it'd be less of an issue if the exercises themselves were not included, but even then, there's a lot of red tape you'll have to navigate.