  In this paper I review the theory and numerical simulations of non-linear
dynamics of preheating, a stage of dynamical instability at the end of
inflation during which homogeneous inflaton explosively decays and deposits its
energy into excitation of other matter fields. I focus on preheating in chaotic
inflation models, which proceeds via broad parametric resonance. I describe a
simple method to evaluate Floquet exponents, calculating stability diagrams of
Mathieu and Lame equations describing development of instability in $m^2\phi^2$
and $\lambda\phi^4$ preheating models. I discuss basic numerical methods and
issues, and present simulation results highlighting non-equilibrium
transitions, topological defect formation, late-time universality, turbulent
scaling and approach to thermalization. I explain how preheating can generate
large-scale primordial (non-Gaussian) curvature fluctuations manifest in cosmic
microwave background anisotropy and large scale structure, and discuss
potentially observable signatures of preheating.
