Marius Mantoiu and Radu Purice The Mathematical Formalism of a Particle in a Magnetic Field (1070K, Postscript) ABSTRACT. In this review article we develop a basic part of the mathematical theory involved in the description of a particle (classical and quantal) placed in the Euclidean space $\mathbb R^N$ under the influence of a magnetic field $B$, emphasising the structure of the family of observables.