The first book of the Advanced Dungeons & Dragons line.
Like the Players Handbook, this has an odd printing history.
The first three printings are actually really easy to tell apart.
1st: Lizardman logo, red centered "Advanced Dungeons & Dragons*" with a small note under that "* TM Reg. Applied For"
2nd: Lizardman logo, red centered "Advanced Dungeons & Dragons(R)"
3rd: Wizard logo, red centered "Advanced Dungeons & Dragons(R)"
After that, it gets a little weird.
For some reason TSR ran out of covers for the third printing long before anything else, so pseudo 4th printing covers were used with 3rd printing interiors. However, the covers actually differed slightly from the 4th printing covers in that there was no ISBN number on the back. More of these were printed than any of the Player's Handbook or Dungeon Master's Guide hybrids, and they are certainly easier to spot.
3.5th: Wizard logo, red upper left corner "Advanced D&D" on yellow band, no ISBN on back. Still says 3rd on title page.
4th: Wizard logo, red upper left corner "Advanced D&D" on yellow band, ISBN on back (three minor variations exist).
5th: Wizard logo, red upper left corner "Advanced D&D TM" on yellow band. Still says 4th on title page.
6th: Face logo, red upper left corner "Advanced D&D TM, Adventure Games" on yellow band. Still says 4th on title page.
7th - 8th: Red Dragon cover. Still ays 4th Edition on title page.
9th and later: Red Dragon Cover. Title page notes printing and date.
Subsequently, "premium" reprints of the book have been made available though they are all clearly marked at such.