  We consider a reduced model of four-dimensional Yang-Mills theory with a mass
term. This matrix model has two classical solutions, two-dimensional fuzzy
sphere and two-dimensional fuzzy torus. These classical solutions are
constructed by embedding them into three or four dimensional flat space. They
exist for finite size matrices, that is, the number of the quantum on these
manifolds is finite. Noncommutative gauge theories on these noncommutative
manifolds are derived by expanding the model around these classical solutions
and studied by taking two large $N$ limits, a commutative limit and a large
radius limit. The behaviors of gauge invariant operators are also discussed.
