Let us use some well-known quotes to capture what is often understood by the term distributed system. The first quote is taken from a respective textbook; it describes a distributed system rather conservatively by both its inner parts and its outer observable surface: 

• A distributed system is a collection of independent computers that appears to its users as a single coherent system. (Andrew S. Tanenbaum)

The second quote comes from one of the more theoretically-minded scientific pioneers of the field; by its emphasis on the point of view of an every-day user, it indicates the one of the subtle key issues of distributed systems:

• A distributed system is one in which the failure of a computer that you didn't even know existed can render your own computer unusable. (Leslie Lamport)

It was also Lamport who pointed out:

• We know of no area in computer science or mathematics in which informal reasoning is more likely to lead to errors than in the study of this type of [distributed] algorithm.

It is precisely statements like the last one that capture the scientific challenge that drive our research unit. To tackle the challenge, we develop and investigate formal mathematical theories that allow us find errors in distributed [software] systems or to prove them correct, i.e., free of errors.