In this book, quantum mechanics is developed from the outset on a relativistic basis, using the superposition principle, Lorentz invariance and gauge invariance. Nonrelativistic quantum mechanics appears as a special case, classical relativistic mechanics as another one. These special cases are important for giving plausible names to operators, for example "orbital angular momentum", "spin" or "magnetic moment". A subject which is treated for the first time in this book is the theory of binaries in terms of differential equations which have the mathematical structure of the corresponding one-body equations (Klein-Gordon for two spinless particles, Dirac for two spinor particles), and which allow the calculation of radiative corrections via the vector potential operator.