  We study the de Haas-van Alphen (dHvA) oscillation in two-dimensional and
quasi-two-dimensional systems. We give a general formula of the dHvA
oscillation in two-dimensional multi-band systems. By using this formula, the
dHvA oscillation and its temperature-dependence for the two-band system are
shown. By introducing the interlayer hopping $t_z$, we examine the crossover
from the two-dimension, where the oscillation of the chemical potential plays
an important role in the magnetization oscillation, to the three-dimension,
where the oscillation of the chemical potential can be neglected as is well
know as the Lifshitz and Kosevich formula. The crossover is seen at $4 t_z \sim
8 ta b H /\phi_0$, where a and b are lattice constants, $\phi_0$ is the flux
quantum and 8t is the width of the total energy band. We also study the dHvA
oscillation in quasi-two-dimensional magnetic breakdown systems. The quantum
interference oscillations such as $\beta-\alpha$ oscillation as well as the
fundamental oscillations are suppressed by the interlayer hopping $t_z$, while
the $\beta+\alpha$ oscillation gradually increases as $t_z$ increases and it
has a maximum at $t_z/t\approx 0.025$. This interesting dependence on the
dimensionality can be observed in the quasi-two-dimensional organic conductors
with uniaxial pressure.
