AERN (Approximating Exact Real Numbers). A Haskell library for rigorous and exact real number and real function computation. AERN aims to make it easy to program rigorous and accurate computations over real numbers, (piecewise continuous) real functions and interval functions. Currently, AERN contains some applications in rigorous ODE solving and hybrid system simulation. AERN is written in Haskell because it focuses on reliability, flexibility and reusability. The main techniques employed are Kaucher arithmetic and automatic polynomial approximation of functions.