Entropy was created after inflation? I'm puzzeled by a statement in Big Bang Cosmology-review about the reheating phase subsequent to the exponential expansion during inflation: 

In this reheating process, entropy has been created and the final value of $RT$ is greater than the initial value of $RT$.

(Taken from section 21.3.5. on page 17.)
How can I reconcile this with the first law of thermodynamics...
 A: There is nothing wrong with that statement (assuming that the meaning is: prior to  inflation we have a total amount X of entropy, then after the inflation we have a lot more than X).
After the inflation, the scalar field (inflaton) is in the minimum of the potential well and is a super-cooled Bose-Einstein condensate whose constituents are very massive scalar bosons. Such system of very cold spin 0 bosons is unstable and is transformed by the decay process into energy of ultrarelativistic species, so that the universe undergoes a strong reheating phase.
The enormous increase in entropy is due to these decays. You can show that (the exact calculation depends on the model you choose) in a given comoving volume $ V $ the increase is something like:
\begin{equation}
S_{post \; Reh} \simeq e^{3 \mathcal{E}} S_{pre \; Inf}
\end{equation}
Usually $ \mathcal{E}\sim 60 $ and this means $ e^{180} \sim 10^{78} $. This result is certainly in agreement with the second law of thermodynamics! There are no contradiction with the first law (anyway you must pay attention to carefully define the quantity you want to use, the entire universe it's not a trivial thermodynamic system)
A: A form of the first law of thermodynamics:

In a thermodynamic process involving a closed system, the increment in the internal energy is equal to the difference between the heat accumulated by the system and the work done by it.

It is a form of conservation of energy.
Thermodynamics developed and has been validated as a theory in the framework of Newtonian mechanics. The Big Bang model, particularly at the inflationary period is dominated by the General Relativity framework. In General Relativity energy conservation is moot, 

In general relativity conservation of energy-momentum is expressed with the aid of a stress-energy-momentum pseudotensor. The theory of general relativity leaves open the question of whether there is a conservation of energy for the entire universe.

One can find a number of discussions on this, and the limits of how energy conservation can be defined. 
