  Second-order topological insulators are crystalline insulators with a gapped
bulk and gapped crystalline boundaries, but topologically protected gapless
states at the intersection of two boundaries. Without further spatial
symmetries, five of the ten Altland-Zirnbauer symmetry classes allow for the
existence of such second-order topological insulators in two and three
dimensions. We show that reflection symmetry can be employed to systematically
generate examples of second-order topological insulators and superconductors,
although the topologically protected states at corners (in two dimensions) or
at crystal edges (in three dimensions) continue to exist if reflection symmetry
is broken. A three-dimensional second-order topological insulator with broken
time-reversal symmetry shows a Hall conductance quantized in units of $e^2/h$.
