What is the order of a reaction?

The order of a reaction in some species seems an obvious, trivial concept that all chemists master. However, in complex situations such as catalytic systems, the order of a reaction is not always that simple: it can be partial, negative and function of other parameters. In order to analyze rate laws and experimental orders of complex reaction networks, it is necessary to have a proper mathematical description of what the order of a reaction is. In general, chemists working in catalysis are unaware that such a mathematical description exists and therefore they are restricted to analyzing only extreme limit cases of rate laws. This manuscript offers a description and a simple demonstration of this concept, known as elasticity coefficient or normalized sensitivity. It also presents several examples of applications on classic and usual catalytic scenarios.