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In this work the asymptotic structure of space-time and the main propertiesof the Bondi-Metzner-Sachs (BMS) group, which is the asymptotic symmetry groupof asymptotically flat space-times, are analysed. Every chapter, except thefourth, begins with a brief summary of the topics that will be dealt through itand an introduction to the main concepts. The work can be divided into threeprincipal parts. The first part includes the first two chapters and is devotedto the development of the mathematical tools that will be used throughout allof the work. In particular we will introduce the notion of space-time and willreview the main features of what is referred to as its causal structure and thespinor formalism, which is fundamental in the understanding of the asymptoticproperties. In the second part, which includes the third, fourth and fifthchapters, the topological and geometrical properties of null infinity, I, andthe behaviour of the fields in its neighbourhood will be studied. Particularattention will be paid to the peeling property. The last part is completelydedicated to the BMS group. We will solve the asymptotic Killing equations andfind the generators of the group, discuss its group structure and Lie algebraand eventually try to obtain the Poincar\'e group as its normal subgroup. Thework ends with a brief conclusion in which are reviewed the main modernapplications of the BMS group.

Asymptotic Structure and Bondi-Metzner-Sachs group in General Relativity