This book offers an essential introduction to the notions of sound wave topology duality
coherence and wave-mixing which constitute the emerging new science of sound. It includes
general principles and specific examples that illuminate new non-conventional forms of sound
(sound topology) unconventional quantum-like behavior of phonons (duality) radical linear and
nonlinear phenomena associated with loss and its control (coherence) and exquisite effects
that emerge from the interaction of sound with other physical and biological waves (wave
mixing). The book provides the reader with the foundations needed to master these complex
notions through simple yet meaningful examples. General principles for unraveling and
describing the topology of acoustic wave functions in the space of their Eigen values are
presented. These principles are then applied to uncover intrinsic and extrinsic approaches to
achieving non-conventional topologies by breaking the time reversal symmetry of acoustic waves.
Symmetry breaking can impart topological immunity to wave degradation from imperfection
scattering and catalyze controlled coherence. In the intrinsic case and the phonon
representation of acoustic waves the self-interaction interference of a wave through its
supporting medium exposes the notion of duality in the quantum statistics (i.e. boson vs.
fermion characterized by the symmetry of multiple particle states) and how the quantum analogue
behaviors of sound can be exploited in the form of novel sound-based information transfer and
processing devices. By considering media that mix different types of waves the book addresses
the interaction of sound with other physical and biological waves but also brings to light
examples of extrinsic processes that can lead to symmetry breaking. The coherent conversion of
sound into other types of waves as well as the sound-induced non-conventional topology of
elastic electronic spin and biological waves are presented in the case of media exhibiting
elasto-electronic photo-elastic magneto-elastic effects and biological mechano-transduction.
