Introduction -- History of Gauge Theory -- Coordinate Systems as the Framework of Equations -- Gauge Fields -- Covariant Derivative in Gauge Theory -- Lie Groups -- Global Gauge Invariance -- Local Gauge Invariance -- Gauge Fixing -- Noether's Theorem -- Spontaneous Symmetry Breaking and Phonon as the Goldstone Mode -- Time Reversal Acoustics and Super resolution -- Negative Refraction, Acoustical Metamaterials , and Acoustical Cloaking -- New Acoustics based on Metamaterials.

This book highlights the symmetry properties of acoustic fields and describes the gauge invariance approach, which can be used to reveal those properties. Symmetry is the key theoretical framework of metamaterials, as has been demonstrated by the successful fabrication of acoustical metamaterials. The book first provides the necessary theoretical background, which includes the covariant derivative, the vector potential, and invariance in coordinate transformation. This is followed by descriptions of global gauge invariance (isotropy), and of local gauge invariance (anisotropy). Sections on time reversal symmetry, reflection invariance, and invariance of finite amplitude waves round out the coverage. .