A researcher discovers and decodes a radio signal from an alien race. She eventually sends a response, and over time, using set theory, logic, and math, humans and the aliens figure out how to communicate. The aliens send a series of questions about ethics and morality. After the researcher answers, they send plans for a biological printer/incubator that can construct individuals of their species, so they can experience what it is like to be a different species.
The round trip time for each radio message is several decades. This is a core issue in the book. At the time this is going on, medicine and life-extension techniques are just starting to reach the "effective immortality point" (life expectancy increasing by more than one year for each year that passes), which is necessary for a single individual to maintain a conversation over light years. In the book, the alien sending the messages only wants to talk to the one specific researcher.
The book references the essay "What is it like to be a bat?" and the science fiction film "Contact".
One of the questions the aliens ask (paraphrased):
You and your friend come across an object while traveling together. It has no value and isn't useful to either of you. You can't leave it behind and you can't share it. Which of you should keep it?