This lecture will describe the mathematical and statistical methods of estimating the errors in the optimal assessment of the past climate change, quantifying the uncertainties in the climate change detection, and analyzing the main uncertainty sources for climate predictions. Empirical orthogonal functions are extensively used to deal with spatial inhomogeneity. Temporal non-stationarity and model nonlinearity will be discussed. Detailed error analyses of the annual mean global and regional averages of the surface air temperature since 1861 will be presented.