  We give a pedagogical review of a covariant and fully non-perturbative
approach to study nonlinear perturbations in cosmology. In the first part,
devoted to cosmological fluids, we define a nonlinear extension of the
uniform-density curvature perturbation and derive its evolution equation. In
the second part, we focus our attention on multiple scalar fields and present a
nonlinear description in terms of adiabatic and entropy perturbations. In both
cases, we show how the formalism presented here enables one to easily obtain
equations up to second, third and higher orders.
