  Perhaps the most important aspect of symmetry in physics is the idea that a
state does not need to have the same symmetries as the theory that describes
it. This phenomenon is known as spontaneous symmetry breaking. In these lecture
notes, starting from a careful definition of symmetry in physics, we introduce
symmetry breaking and its consequences. Emphasis is placed on the physics of
singular limits, showing the reality of symmetry breaking even in small-sized
systems. Topics covered include Nambu-Goldstone modes, quantum corrections,
phase transitions, topological defects and gauge fields. We provide many
examples from both high energy and condensed matter physics. These notes are
suitable for graduate students.
