In what ways is memory important and how does it contribute to a theme in the novel?

The idea of memory in the story is directly related to the
themes of isolation and destruction.  As a
result of the third-person and mostly omniscient point-of-view, the reader is invited
into the much more complex inner workings and personality of Edgar than his actions and
limited communication reveal of him to others.  Memory plays a key role in this
complexity.

At the very beginning of the story, the reader
is introduced to images of Almondine in what would be Edgar's "earliest memory,"
suggesting that even as a baby, Edgar has an accute perception of his dog, one which
sticks with him for life.  As the mute only child of two arguably introverted parents,
Edgar's isolation from the world outside of the dog kennel seems to be almost created
and fostered by his circumstances.  As a result, Edgar often lives very much inside his
own head.  He is frequently reflective on his own past, and very much interested in the
past of his parents (one which they never share the complete truth of, but the stories
of which almost become as dear to him as his own memories).  He is both happy and
seemingly healthy.

When his father mysteriously dies and
Edgar is the only witness, he cannot remember the details of his father's final moments
clearly enough to recall them to Glen (the town policeman).  It is as if his mind is
blocking the memory to protect him.  Soon after, when his father's ghost visits Edgar in
the kennel, Edgar experiences a physical sensation that the ghost has touched his heart
and given him all of his father's memories.  The feeling is so powerful Edgar thinks it
might kill him.  For one instant he holds complete understanding of who his father is
and what his intentions always were, but in the next instant, the feeling, and the
memories, are gone.  He wakes the next morning wondering if it was all a dream.  He now
harbors a secret he cannot explain to anyone, because he's not even completely sure of
the reality of it himself.  His isolation increases and so begins his
destruction.

When he runs away from home, his memories
haunt him.  Because he is isolated from all other humans, all he has is time to think of
the past.  Memories of Almondine are the worst because they are the most tangible and
realistic.  If he dwells on them, dread and despair threaten to crush him.  At night, he
dreams of his father and thrashes in his sleep, but wakes up unable to remember any
details of the dream.  He is constantly thinking of memories of his mother and Claude,
and looking for clues in the memories to further understanding his father's death (and
how he can explain it).  He constantly fears forgetting more and hates himself for the
things he cannot recall.

In many ways, the author uses the
memory motif as a means of setting up characters who, though far from
ordinary, are certainly happy and healthy.  Even in his isolation,
when his father is alive, Edgar is both.  Then, the same motif is used to show how a
death in the family can immediately plague the happiness and health of the survivors. 
Edgar's isolation evolves from something that was once something he lived with, to
something he fears will kill him.