  This Tutorial will introduce the mathematical framework for describing
systems of identical particles, and explain the notion of indistinguishability.
We will then focus our attention on dynamical systems of free particles and
formally introduce the concept of many-particle interference. Its impact on
many-particle transition probabilities is computationally challenging to
evaluate, and it becomes rapidly intractable for systems with large numbers of
identical particles. Hence, this Tutorial will build up towards alternative,
more efficient methods for observing signatures of many-particle interference.
A first type of signatures relies on the detection of a highly sensitive -but
also highly fragile-processes of total destructive interference that occurs in
interferometers with a high degree of symmetry. A second class of signatures is
based on the statistical features that arise when we study the typical
behaviour of correlations between a small number of the interferometer's output
ports. We will ultimately show how these statistical signatures of
many-particle interference lead us to a statistical version of the
Hong-Ou-Mandel effect.
