  We present a brief description of noncompactified higher-dimensional theories
from the perspective of general relativity. More concretely, the
Space-Time-Matter theory, or Induced Matter theory, and the reduction procedure
used to construct the modified Brans-Dicke theory and the modified
S\'{a}ez-Ballester theory are briefly explained. Finally, we apply the latter
to the Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) cosmological models in
arbitrary dimensions and analyze the corresponding solutions.
