The most general description of a chemical reaction network considers a number  of distinct chemical species reacting via  reactions.
 The chemical equation of the -th reaction can then be written in the generic form
which is often written in the equivalent form
Here
*  is the reaction index running from 1 to ,
*  denotes the -th chemical species,
*  is the rate constant of the -th reaction and
*  and  are the stoichiometric coefficients of reactants and products, respectively.
The rate of such a reaction can be inferred by the law of mass action
which denotes the flux of molecules per unit time and unit volume. Here  is the vector of concentrations. This definition includes the elementary reactions:
; zero order reactions
:for which  for all ,
; first order reactions
:for which  for a single ,
; second order reactions
:for which  for exactly two ; that is, a bimolecular reaction, or  for a single ; that is, a dimerization reaction.
Each of these is discussed in detail below. One can define the stoichiometric matrix
denoting the net extent of molecules of  in reaction . The reaction rate equations can then be written in the general form
This is the product of the stoichiometric matrix and the vector of reaction rate functions.
Particular simple solutions exist in equilibrium, , for systems composed of merely reversible reactions. In this case, the rate of the forward and backward reactions are equal, a principle called detailed balance. Detailed balance is a property of the stoichiometric matrix  alone and does not depend on the particular form of the rate functions . All other cases where detailed balance is violated are commonly studied by flux balance analysis, which has been developed to understand metabolic pathways.