Rational homotopy theory, I

Rational homotopy theory is a branch of homotopy theory focused on the study of spaces “modulo torsion”. Roughly, this consists of two steps. First, one “kills” all torsion phenomena of a given space in a nice way – by a process called the “rationalization”, or “localization at the empty set of primes”. Second, one finds algebraic models that faithfully capture the homotopy type of this rationalization, and which are amenable to computations.