This monograph deals with cases where optimal control either does not exist or is not unique cases where optimality conditions are insufficient of degenerate or where extremum problems in the sense of Tikhonov and Hadamard are ill posed and other situations A formal application of classical optimisation methods in such cases either leads to wrong results or has no effect The detailed analysis of these examples should provide a better understanding of the modern theory of optimal control and the practical difficulties of solving extremum problems