What is the conflict in The Twenty One Balloons, and who are the main characters?

Professor William Waterman Sherman is the main character
of the story.  After chapter one, he also becomes the story's
narrator.  He is sixty-six years old, and a retired arithmetic
teacher, from San Francisco.  In the first year of his retirement, he decides to build
and fly a hot air balloon, and hopes to be the first man to fly across the Pacific
Ocean.

While there are several smaller conflicts within the
greater context of the story, the main conflict occurs when his
balloon is punctured by a seagull, and crashes on the island of Krakatoa.  This island
is actually an active volcano, which is about to experience a massive (and historically
accurate) eruption.

There are several minor characters that
Professor Sherman meets while stranded on Krakatoa, who are members of the 20 families
that inhabit the place.  These families live in a secret and wealthy utopian society,
and each are named for a letter of the alphabet, from A on down.