  The statistical mechanics of a system of non-relativistic charged particles
in a constant magnetic field is discussed. The spatial dimension $D$ is
arbitrary with $D\geq 3$ assumed. Calculations are presented from first
principles using the effective action method. For $D\geq 5$ the system has a
phase transition with a Bose condensate. We show how the effective action
method method deals with in a very natural way with the condensate and study
it's r\^{o}le in the magnetization of the gas. For large values of the magnetic
field we show how the magnetized gas in $D$ spatial dimensions behaves like the
free Bose gas in $(D-2)$ spatial dimensions. Even though for D=3 the magnetized
gas does not have a phase transition for any non-zero value of the magnetic
field, we show how the specific heat starts to resemble the result for the free
gas as the magnetic field is reduced. A number of analytical approximations for
the magnetization and specific heat are given and compared with numerical
results. In this way we are able to study in precise detail how the $B\to 0$
limit of the magnetized gas is achieved.
