When dealing with kinetics, the mechanism or actual pathway followed is required for all chemical equations. If the reaction proceeds exactly as written, it is called elementary.
Usually reactions must be viewed as a series of steps that ultimately combine into the final product. Each of these steps provide insight into the factors that determine the overall speed of the reaction, including the formation of intermediates, species found inside the reaction but do not appear in the final products.Regardless of whether a reaction is elementary or one particular step, there are four important equations that can be determined. I separate them by the following names:

1. Individual Rate of Reaction
2. Overall Rate of Reaction
3. Rate Law
4. Activation Energy

Individual rate of reaction

The individual rate of reaction is the change in the concentration over the change in time of a specific species. To distinguish between a reactant and product, the rate is either called:  formation, mathematically given a positive sign, or consumption and is assigned a negative sign.
Figure 9.1 (above) shows the individual rates of reactions for the equation A + 3B → 2Y.
These equations are limited to individual species with known concentration changes.

Overall rate of reactions

Overall rate of reactions show how all species in a reaction are related using their individual stoichiometry. Section 9.2 of the Physical Chemistry book has a wonderful interactive clip on chemical kinetics, that allows this stoichiometry to be changed and the resulting equation.

These equations show how each species relates to the others and ultimately to the overall rate of reaction.
The reaction rate goes one step further and relates the rate with the importance or order of each reactant. This order is not the coefficient but must be determined experimentally. This equation adds a new variable, the rate constant that takes into account certain characteristics of the reaction.
The following table relates the different forms of the rate of reaction for A+ 3B → 2Y.

By determining the order of the reaction (or lack of order), the power of prediction has been opened because each order has specific characteristics that are fixed and allows the determination of half-lives.

Rate law

Integrating the rate law and plotting the concentration vs. time, the plot with a straight line determines the order. A straight line equation can then be calculated and used to determine a half-life equation and predict other times and concentrations.
The following table lists the characteristics of a single reactant equation A → Product.

Section 9.3, of the Physical Chemistry book, has an interactive multimedia clip that shows the three most common orders:  zero, first and second.
Each of these first three equations deal with the same rate, regardless of what the equation is called! The only thing that is changing is the form it is discussed in.

Activation Energy

In order for a reaction to be successful the reactants must have the proper orientation and the proper amount of kinetic energy that will allow chemical bonds to break or form. The minimum amount of energy required is called the activation energy, E_a. In order to find the activation energy, temperature must be taken into account, leading to the fourth equation.
The rate constant can be discussed in terms of activation energy in the Arrhenius equation, k = Ae^-Ea\RT and integrated to get the straight line equation:  ln k = ln A – E_a/RT.  A linear plot of rate constant vs. 1/temperature would yield a slope that contains the activation energy and is discussed in section 9.7, of the ebook, with an interactive clip that allows the changing of temperatures.
This covers the basics in discussing a single reaction, whether elementary or one particular step. Chapter 10 (chp 9 and 10 form the kinetics module) deals with reactions with more than one step (complex, composite or stepwise) and how they are viewed.