The Globe Illustrated Shakespeare: The Complete Works was an annotated hardbound book that contained all works written by William Shakespeare. Jean-Luc Picard owned a copy of this book and kept it under a glass cover in his ready room.
The copy used on the set was the 1986 Greenwich House edition, specifically the version with authentic leather binding (ISBN 0-517-623803). Written and annotated by Howard Staunton (1810-1874), it was attractively bound, but that version is generally looked upon by Shakespearean scholars today as being outdated in terms of its scholarship.
The book was only on display in Picard's ready room until TNG: "Coming of Age". Beginning with TNG: "The Arsenal of Freedom", it was replaced by Volume I (and later Volume II) of The Annotated Shakespeare. After that, it appears in his quarters in a few season 2 episodes and is seen in his quarters aboard the USS Enterprise-E in Star Trek: Insurrection and in the Starfleet Museum Quantum Archives in PIC: "Remembrance".
Patrick Stewart, who played Captain Picard, is a noted Shakespearean actor, and was in the Royal Shakespeare Company for a number of years. He made his Broadway debut in Peter Brook's production of A Midsummer Night's Dream.