Even though the book is a collection of short stories, they are tied together with a central theme of character vs. society and character vs. technology. 

The main conflict in the collection of short stories called The Martian Chronicles is character vs. society.  In all cases, the people who go to Mars are either looking for something or trying to get away from something.  Most come to Mars because they are not happy with life on Earth.

One example of disenchantment with Mars is seen through the captain in “The Earth Men.”

For two cents I’d go back home and tell people not to bother with Mars.  What a suspicious bunch of louts. (p. 37)

In “There Will Com Soft Rains” we are given a glance at another concept of Earth.  In this story, a home in Allendale, California continues to operate in a fully automated fashion long after the people have disintegrated into stains from some nuclear blast.

The house stood alone in a city of rubble and ashes. This was the one house left standing. At night the ruined city gave off a radioactive glow which could be seen for miles. (p. 221)

The conflict here is that people have destroyed themselves, and yet their automation goes on.  Their society destroyed them.

The common threat in all of these stories is that life on Earth is not pleasant, and people go searching for something else.  They do not usually find it.  By the time we get to the end of the stories, Earth has been destroyed too