The Gray Book is a fan-edit/compilation of the original D&D rules.
Excerpt from a blog entry on RetroRoleplaying:"
[The Gray Book]...is a collected, re-organized and slightly edited version of the OD&D rules and supplements (with some additions from The Strategic Review, The Dragon #1, Holmes D&D, Basic/Expert D&D, and even AD&D).
In spite of the additional material, The Gray Book has a house-ruled OD&D and supplements feel. The only major feature I noticed missing from OD&D and its three rules supplements is psionics. I could have easily used The Gray Book back in the late 1970s to run my OD&D games instead of OD&D, Greyhawk, Blackmoor, and Eldritch Wizardry.