  We derive a systematic high-frequency expansion for the effective Hamiltonian
and the micromotion operator of periodically driven quantum systems. Our
approach is based on the block diagonalization of the quasienergy operator in
the extended Floquet Hilbert space by means of degenerate perturbation theory.
The final results are equivalent to those obtained within a different approach
[Phys.\ Rev.\ A {\bf 68}, 013820 (2003), Phys.\ Rev.\ X {\bf 4}, 031027 (2014)]
and can also be related to the Floquet-Magnus expansion [J.\ Phys.\ A {\bf 34},
3379 (2000)]. We discuss that the dependence on the driving phase, which
plagues the latter, can lead to artifactual symmetry breaking. The
high-frequency approach is illustrated using the example of a periodically
driven Hubbard model. Moreover, we discuss the nature of the approximation and
its limitations for systems of many interacting particles.
