Rational homotopy theory is homotopy theory modulo torsion. This simplification reduces topology to algebra. More precisely, Quillen proved that the rational homotopy theory of 2-connected spaces is equivalent to that of (1) 1-connected dg Lie algebras (2) 2-connected dg cocommutative coalgebras. This is subsequently augmented by Sullivan, who provides a dg commutative algebra model of rational homotopy theory with computational strength. Time permitting, I will also discuss interesting applications to geometry and local algebra.