  These notes illustrates the power of formulating ideas of commutative algebra
in a homotopy invariant form. They can then be applied to derived categories of
rings or ring spectra. These ideas are powerful in classical algebra, in
representation theory of groups, in classical algebraic topology and elsewhere.
  The notes grew out of a series of lectures given during the `Interactions
between Representation Theory, Algebraic Topology and Commutative Algebra'
(IRTATCA) at the CRM (Barcelona) in Spring 2015.
