  Fair division is the problem of dividing one or several goods amongst two or
more agents in a way that satisfies a suitable fairness criterion. These Notes
provide a succinct introduction to the field. We cover three main topics.
First, we need to define what is to be understood by a "fair" allocation of
goods to individuals. We present an overview of the most important fairness
criteria (as well as the closely related criteria for economic efficiency)
developed in the literature, together with a short discussion of their
axiomatic foundations. Second, we give an introduction to cake-cutting
procedures as an example of methods for fairly dividing a single divisible
resource amongst a group of individuals. Third, we discuss the combinatorial
optimisation problem of fairly allocating a set of indivisible goods to a group
of agents, covering both centralised algorithms (similar to auctions) and a
distributed approach based on negotiation.
  While the classical literature on fair division has largely developed within
Economics, these Notes are specifically written for readers with a background
in Computer Science or similar, and who may be (or may wish to be) engaged in
research in Artificial Intelligence, Multiagent Systems, or Computational
Social Choice. References for further reading, as well as a small number of
exercises, are included.
  Notes prepared for a tutorial at the 11th European Agent Systems Summer
School (EASSS-2009), Torino, Italy, 31 August and 1 September 2009. Updated for
a tutorial at the COST-ADT Doctoral School on Computational Social Choice,
Estoril, Portugal, 9--14 April 2010.
