It is difficult to discuss the two major themes of the novel - the search for order and stability and the role of absence in life - because the search for order in this novel often involves the acknowledgment and filling of an absence. The theme of the search for order and stability in life develops subtly but is changed radically when the presence of the second mystery is revealed - an absence. While it seems that the story is about the search for Wellington's murderer, most all the clues that Christopher discovers also seek to answer an absence he isn't even aware exists: the status and whereabouts of his mother Judy. This is the true "curious incident of the dog in the night-time" - the incident which is significant precisely because nothing happens, it is the absence which points to a deeper truth. The solving of the two mysteries are only the prologue to the true fulfillment of order in Christopher's life: a reunion with his mother and the restoration of a more balanced family order, as well as the successful completion of his A-level math exam to pave his planned future as a scientist.
Further, it should be noted this is not a story about "overcoming" a disease, but rather of living with a specific condition. The triumph does not hinge on acting as if this condition doesn't exist but in working with that condition to lead as rich a life as possible. Christopher makes no attempt to pretend he is anything other than he is, nor is there any encouragement to do so by the people around him. This is played subtly, since the kind of autism that Christopher suffers from - Asperger's Syndrome - is never named in the text and the exact clinical parameters of his condition are never explained. As we see things from within his perspective, these are things he would take for granted as just how his life is and how his mind works. Stability and order, then, isn't the removal of all obstacles in life, but dealing with the situation one is given.
As for the theme of absence, it manifests in various ways throughout the book. The loneliness of Ed Boone is brought up subtly, in his failed romance with Mrs. Shears and the pornography that he keeps in his bedroom. A larger absence occurs when he loses his son's trust after his deception is revealed - this is accentuated by Christopher's refusal to speak or touch his father in the latter half of the book. Christopher is given his own taste of absence, not when his mother dies, but when he realizes she is still alive and thus still within reach. Further, his decision to leave Swindon and all that's familiar provokes new emotions in Christopher: he feels heartache and longing for home, further accentuated once he goes to London and loses such things as the nighttime stars and a garden. The restoration of a new family order and Christopher's continued success intellectually help fill this loneliness, as father and son work to re-establish trust at the end of the novel.
Related to these major themes are various minor themes which spring from Christopher's basic struggle.
There is the theme of family: the story begins with a truncated family unit of son and widower father, seemingly stable and happy. However, we also get a hint that there was a maternal figure in Mrs. Shears after Judy Boone "died" but this did not work out; we also are told that when she was around, Christopher's mother was not as patient a mother as she needed to be. Finally, the notion of a stable family is disrupted in both the past and present: we find out that two years earlier, Judy Boone had an affair with Roger Shears and ran off with him; and we find out that in the present day, Ed Boone has been hiding from Christopher that his mother is indeed alive, a lie which shatters the trust between father and son. Christopher goes on to seek a new stability with a reconstituted family: another dyad, this of mother-son in London instead of father-son in Swindon. Unfortunately, there is also a potential father figure in Roger Shears who stands in the way of this new dyad; motherhood finally usurps misguided romance, however, as Mr. Shears is quickly jettisoned by Judy Boone.
All these permutations of family are exposed as being unbalanced, either by a lack of patience or deception. But from here, an uneasy but ultimately productive equilibrium is reached in the family structure. Christopher and his mother return to Swindon from London, which is itself a return to stability. Judy becomes the main caretaker for Christopher, but Ed Boone begins a project to re-establish trust with his son. Christopher has both parents again: a mother who has re-asserted her claim to her son and the responsibilities involved; and a father whose patience will allow a new trust to develop.
The theme of mathematics and science as a source of order and stability in Christopher's life. They provide a framework not only to simplify aspects of his life, but also to safely consider how complex life is, as seen by his view of how prime numbers are like life and the example of the Monty Hall Problem. As another example, Christopher is reading James Gleick's best-selling popular science book Chaos at one point in the novel: far from being about disorder, the book deals with chaos theory and how seemingly random events are actually ordered in a highly complex but logical manner. Chaos is thus tamed by Chaos, an irony Christopher can appreciate.
Throughout the novel, Christopher uses math to explain things which could otherwise prove frustrating or difficult; it also gives him something to focus on when he is under extreme stress, such as during his trip to London or when his parents argue. In this sense this theme doesn't change from start to finish - this is a fixed part of his personality, and one that he stakes his future upon. In that light, the most obvious development in this theme is Christopher's success in taking A-level maths and his plans to become a scientist.