  The aim of this work is to present a series of concrete examples which
illustrate how the computer algebra system Cadabra can be used to manipulate
expressions appearing in General Relativity and other gravitational theories.
We highlight the way in which Cadabra's philosophy differs from other systems
with related functionality. The use of various new built-in packages is
discussed, and we show how such packages can also be created by end-users
directly using the notebook interface.
  The current paper focuses on fairly generic applications in gravitational
theories, including the use of differential forms, the derivation of field
equations and the construction of their solutions. A follow-up paper discusses
more specific applications related to the analysis of gravitational waves.
