  We introduce the notion of locally trivial quantum principal bundles. The
base space and total space are compact quantum spaces (unital
$C^{\star}$-algebras), the structure group is a compact matrix quantum group.
We prove that a quantum bundle admits sections if and only if it is trivial.
Using a quantum version of \v{C}ech cocycles, we obtain a reconstruction
theorem for quantum principal bundles. The classification of bundles over a
given quantum space as a base space is reduced to the corresponding problem,
but with an ordinary classical group playing the role of structure group. Some
explicit examples are considered.
