The Vulkan Programming Guide: The Official Guide to Learning Vulkan book written by AMD's Graham Sellers and Google's John Kessenich is now up for pre-orders. This appears to be the first official book written about the next-generation Khronos graphics API.
The cover is very similar to the famed OpenGL red book.
The 900-page paperback book covers everything you need to know about the Vulkan graphics API. Both authors have been heavily involved in the Vulkan working group.
The book is now available for pre-order with a listed release date of 4 August 2016. It doesn't mean that Vulkan isn't going to be released until then, but that's just when the book is going to be out. Vulkan will be out once the legal review is over and there are "product quality" implementations. We can hope that Vulkan is released around GDC in March as an annual, major event for Khronos, but there has been no official word on when this new API will be out.
If you want to pre-order this Vulkan programming book, you can do so over on Amazon.com.