This book consists of the articles published in the special issues of this Symmetry journal based on two-by-two matrices and harmonic oscillators.  The book also contains additional articles published by the guest editor in this Symmetry journal.  They are of course based on harmonic oscillators and/or two-by-two matrices.  The subject of symmetry is based on exactly soluble problems in physics, and the physical theory is not soluble unless it is based on oscillators and/or two-by-two matrices.  The authors of those two special issues were aware of this environment when they submitted their articles.  This book could therefore serve as an example to illustrate this important aspect of symmetry problems in physics.