TUnfold is a tool for correcting migration and background effects in high energy physics for multi-dimensional distributions. It is based on a least square fit with Tikhonov regularisation and an optional area constraint. For determining the strength of the regularisation parameter, the L-curve method and scans of global correlation coefficients are implemented. The algorithm supports background subtraction and error propagation of statistical and systematic uncertainties, in particular those originating from limited knowledge of the response matrix. The program is interfaced to the ROOT analysis framework.