  This text is a detailed overview of the theories of W*-algebras and
noncommutative integration, up to the Falcone-Takesaki theory of noncommutative
Lp spaces over arbitrary W*-algebras, and its extension to noncommutative
Orlicz spaces. The topics under consideration include the Tomita-Takesaki
modular theory, the relative modular theory (featuring bimodules, spatial
quotients, and canonical representation), the theory of W*-dynamical systems
(featuring derivations, liouvilleans, and crossed products), noncommutative
Radon-Nikodym type theorems, and operator valued weights. We pay special
attention to abstract algebraic formulation of all properties (avoiding the
dependence on Hilbert spaces wherever it is possible), to functoriality of
canonical structures arising in the theory, and to the relationship between
commutative and noncommutative integration theories. Several new results are
proved.
