Kurt Vonnegut is one of those science fiction writers who has been fortunate enough to be read and respected outside his own genre. This is one of the reasons why: his second novel, and a really good example of his particular style and storylines.
The novel tells the story of a 22nd century American billionaire, Malachi, who is contacted by Rumfoord, a mysterious human space traveller trapped in a strange inter-dimensional state. Rumfoord predicts a strange and disturbing future for Malachi which he goes to great lengths to avoid, only to haplessly bring this future about. In it he finds himself in a relationship with Rumfoord's estranged wife then on a journey to Mars, conscripted into the Martian forces for a war with Earth and then catapulted on a series of even stranger journeys. All this seems to have been manipulated by Rumfoord, who can see the past and future all at once and tells people only those parts of it that suit his as yet unclear agenda. It also seems to link to a traveller from a distant galaxy who has been stranded here for 200 thousand years.
This is a good starting point if you want to read Vonnegut, as it introduces characters and concepts that he brings back and develops in some of his later books. It's also a terrific story in its own right, full of satirical touches about human history, religion and politics. He tackles big themes such as free will, but these are all part of the story. His writing style is very amusing and seemingly offhand, but the whole book is very well put together and it all (kind of) makes sense by the end. It's a good start for getting into the slightly fatalistic style Vonnegut uses to express his ideas, the feeling that while we should all think and act for ourselves, we are all at the mercy of something bigger.
It's a classic novel of late 50s Sci Fi and it influenced other writers, especially Douglas Adams. Buy it if you like big ideas explored from unusual angles, and a quirky narrator.