Operator Approximant Problems Arising from Quantum Theory What this book is about: approximants Preliminaries Self adjoint and positive approximants Commutator approximants Spectral and numerical range approximants Unitary isometric and partially isometric approximation of positive operators This book offers an account of a number of aspects of operator theory mainly developed since the 1980s whose problems have their roots in quantum theory. The research presented is in non commutative operator approximation theory or to use Halmos terminology in operator approximants. Focusing on the concept of approximants this self contained book is suitable for graduate courses