This book highlights designs, implementations and applications of tracking differentiator (TD) algorithms. The real-time differentiation estimation of a given signal is of high importance in control science and engineering. A good differentiator shall have i) robustness against input noises and ii) exactness with a small phase delay. The book has three focuses:Designing practical, accurate and efficient TD based on discrete-time optimal control (DTOC).Presenting full convergence analysis on DTOC-TDs.