  Partial cubes are isometric subgraphs of hypercubes. Structures on a graph
defined by means of semicubes, and Djokovi\'{c}'s and Winkler's relations play
an important role in the theory of partial cubes. These structures are employed
in the paper to characterize bipartite graphs and partial cubes of arbitrary
dimension. New characterizations are established and new proofs of some known
results are given.
  The operations of Cartesian product and pasting, and expansion and
contraction processes are utilized in the paper to construct new partial cubes
from old ones. In particular, the isometric and lattice dimensions of finite
partial cubes obtained by means of these operations are calculated.
