  Clusters of galaxies generally form by the gravitational merger of smaller
clusters and groups. Major cluster mergers are the most energetic events in the
Universe since the Big Bang. Some of the basic physical properties of mergers
will be discussed, with an emphasis on simple analytic arguments rather than
numerical simulations. Semi-analytic estimates of merger rates are reviewed,
and a simple treatment of the kinematics of binary mergers is given. Mergers
drive shocks into the intracluster medium, and these shocks heat the gas and
should also accelerate nonthermal relativistic particles. X-ray observations of
shocks can be used to determine the geometry and kinematics of the merger. Many
clusters contain cooling flow cores; the hydrodynamical interactions of these
cores with the hotter, less dense gas during mergers are discussed. As a result
of particle acceleration in shocks, clusters of galaxies should contain very
large populations of relativistic electrons and ions. Electrons with Lorentz
factors gamma~300 (energies E = gamma m_e c^2 ~ 150 MeV) are expected to be
particularly common. Observations and models for the radio, extreme
ultraviolet, hard X-ray, and gamma-ray emission from nonthermal particles
accelerated in these mergers are described.
