Gödel, Escher, Bach: An Eternal Golden Braid by Douglas Hofstadter is an intricate and complex study of Strange Loops, Meta-Concepts in general and their connection to self-awareness and intelligence. Each chapter is separated from the next by a short fictional piece in the style of Lewis Carroll, which exemplifies the theme of the following chapter.
Breather Episode: The interlude "English French German Suite", consisting of Lewis Carroll's poem "Jabberwocky" in three languages, taking place between two chapters of theories on how the human mind works.
She's a Man in Japan: The Tortoise is referred to as male in the original, but the French word for tortoise is the feminine tortue. Hofstadter, who is interested in the phenomenon of unconscious sexism in language, was delighted when this was pointed out, and gave the French translators the go-ahead to make the Tortoise a female character.
Self-Deprecation: A book about "metal-logic", called Copper, Silver, Gold: an Indestructible Metallic Alloy is mentioned in the dialogues. The Crab says that it's "filled with strange Dialogues about many subjects, including molecular biology, fugues, Zen Buddhism, and heaven knows what else." Achilles responds that "probably some crackpot wrote it". The book is also listed in the bibliography, where it's called "a formidable hodge-podge, turgid and confused". Indeed very little praise is given to its author, Egbert B. Gebstadter.
Self-Fulfilling Prophecy: Commented on if a psychic who could determine the minds of other people was allowed to choose his or her jury if accused.
To Be Continued: The two Dialogues Prelude... and ... Ant Fugue are, well, two sections of a separated story. The end of the former ends with TTortoise [sic], while the latter begins with Achilles and CCrab [sic], using "ATTACCA" note in music, an instruction meaning "continue straight on without a break" as a guide.
Viewers Are Geniuses: The dialogues, especially, conceal mathematical jokes that aren't explained in the text. For example, in a spoof of Fermat's Last Theorem, the Tortoise claims to have found a counterexample in which the exponent n is "the only positive integer which does not occur anywhere in the continued fraction for pi". Mathematically inclined readers will know that, while the famous constants e and sqrt(2) have highly patterned continued fractions, that for pi is quasi-random, so the Tortoise's claim is of no help at all in finding the value of n.