This work is a pedagogical review dedicated to a modern description of the
Bondi-Metzner-Sachs group. The curved space-times that will be taken into
account are the ones that suitably approach, at infinity, Minkowski space-time.
In particular we will focus on asymptotically flat space-times. In this work
the concept of asymptotic symmetry group of those space-times will be studied.
In the first two sections we derive the asymptotic group following the
classical approach which was basically developed by Bondi, van den Burg,
Metzner and Sachs. This is essentially the group of transformations between
coordinate systems of a certain type in asymptotically flat space-times. In the
third section the conformal method and the notion of asymptotic simplicity are
introduced, following mainly the works of Penrose. This section prepares us for
another derivation of the Bondi-Metzner-Sachs group which will involve the
conformal structure, and is thus more geometrical and fundamental. In the
subsequent sections we discuss the properties of the Bondi-Metzner-Sachs group,
e.g. its algebra and the possibility to obtain as its subgroup the Poincar\'e
group, as we may expect. The paper ends with a review of the
Bondi-Metzner-Sachs invariance properties of classical gravitational scattering
discovered by Strominger, that are finding application to black hole physics
and quantum gravity in the literature.Comment: 62 pages, 9 figures. Misprints have been amended and two important
references have been adde
