The aim of this paper is to study the local and the global thermodynamic properties of the 3-dimensional rotating Gauss-Bonnet BTZ black hole. We are interested in deriving the conditions for local and global thermodynamic stability of the solution in a given ensemble of state quantities. It is well-known that determining the local thermodynamic stability requires the calculation of the specific heats of the system. We identify the regions of stability for every physical specific heat together with the existing Davies curves. In addition to the local analysis, we generalize the notion of global thermodynamic stability from the standard thermodynamics to describe the global equilibrium of black holes. Here, we apply a proper Legendre transformation of the energy or the entropy to find the natural thermodynamic potential for the given ensemble of macro parameters. The global stability analysis is now conducted on the properties of the new thermodynamic potential. The advantage of this method is that it allows one to chose different potentials, corresponding to different constraints to which the system may be subjected. Finally, we find it natural to impose global thermodynamic stability only where local one exists for the given black hole solution.