Dirac’s theory of constrained systems is outlined. How to deal with dynamics when the number of variables is larger than the true degrees of freedom is at issue. Starting from a familiar classical mechanics with Lagrange multipliers, we classify constraints into the first-class and the second-class. Potential confusions due to the latter are handsomely dealt with by an introduction of the Dirac bracket, on which we spend much effort with an emphasis on mechanics examples. The former, on the other hand, is more relevant for the bulk of the volume for field theories with gauge redundancies, as is the case with Yang-Mills theories and General Relativity. Maxwell theory is invoked as a prototype, with the Gauss constraint given a unique meaning as a generator of the gauge redundancy, and Chern-Simons theory is also offered as a field theory example equipped with both types of constraints.