  We explore the complex associated to a link in the geometric formalism of
Khovanov's (n=2) link homology theory, determine its exact underlying algebraic
structure and find its precise universality properties for link homology
functors. We present new methods of extracting all known link homology theories
directly from this universal complex, and determine its relative strength as a
link invariant by specifying the amount of information held within the complex.
  We achieve these goals by finding a complex isomorphism which reduces the
complex into one in a simpler category. We introduce few tools and methods,
including surface classification modulo the 4TU/S/T relations and genus
generating operators, and use them to explore the relation between the
geometric complex and its underlying algebraic structure. We identify the
universal topological quantum field theory (TQFT) that can be used to create
link homology and find that it is ``smaller'' than what was previously reported
by Khovanov. We find new homology theories that hold a controlled amount of
information relative to the known ones.
  The universal complex is computable efficiently using our reduction theorem.
This allows us to explore the phenomenological aspects of link homology theory
through the eyes of the universal complex in order to explain and unify various
phenomena (such as torsion and thickness). The universal theory also enables us
to state results regarding specific link homology theories derived from it. The
methods developed in this thesis can be combined with other known techniques
(such as link homology spectral sequences) or used in the various extensions of
Khovanov link homology (such as sl_3 link homology).
