We shall be learning that there are two sorts of free energy.
There is the Helmholtz free energy. Commonly used symbols for this are A (from the German die Arbeit – work) or F.
And there is the Gibbs free energy. Commonly used symbols for this are G − or F!
It is unfortunate that some writers will use simply the term "free energy”, using the symbol F, without specifying which, or even giving evidence that they are aware of the difference. I have seen the symbol F used about equally often for Helmholtz, Gibbs or unspecified free energies.
In these notes I shall use the symbol A for the Helmholtz free energy and G for the Gibbs free energy, and I shall avoid the symbol F.