Rudolph Hess makes his first appearance in the book as Hitler's "close friend" and "devoted follower" (1.2.76). In the early days of the Nazi Party, he served as Hitler's personal secretary, and later he became the deputy leader of the Nazi Party.
Shirer writes that throughout his long career with the Nazi Party, Hess "remained a man of limited intelligence," and was "always receptive to crackpot ideas, which he could adopt with great fanaticism" (1.2.79). As Shirer suggests, those qualities may have had something to do with the fact that Hess also remained "one of Hitler's most loyal and trusted followers and one of the few who was not bitten by consuming personal ambition" (1.2.79).
In 1941, Hess disgraced himself in Hitler's eyes—and in the eyes of the Nazi Party—when he commandeered a German fighter plane and flew secretly to Scotland with a harebrained scheme to negotiate peace with the Allies.
Shirer characterizes Hitler as being "shaken to the bone" by Hess's actions: "His closest personal confidant, the deputy leader of the Nazi Party, the second in line to succeed him after Goering, the man who had been his devoted and fanatically loyal follower since 1921 and, since Roehm's murder, the nearest there was to a friend, had literally flown the coop and gone to parley with the enemy!" (4.23.250)
Although Hitler soon accepted that Hess wasn't actually attempting to betray him, he decided that "his trusted lieutenant had simply cracked up" (4.23.266). That was the official story that the Nazis released to the German public, and Hess, for his part, remained in the custody of the Allies until after the war. At the Nuremberg Trials, he was sentenced to life imprisonment (Epilogue.8).