Brownie (and RBrownie) both depend on the GNU Scientific Library (GSL). This tutorial will go though how to install it in various operating systems.
Linux
Many linux distributions such as Ubuntu and OpenSUSE have great package management systems which probably contain GSL packages. If you use these operating systems then you probably know how to use their package managers. This is the recommend way to install the GSL in linux.
Otherwise, you'll have to download the GSL source manually:
gsl/ directory and click on itgsl-VERSION.tar.gz file, where version is 1.14 or greater. Click on that file to download it.tar -xzf gsl-VERSION.tar.gz and then cd to the ./gsl-VERSION directory./configure, then make, and then make install (and you might have to login as the superuser (sudo)
NOTE: You will want to build the GSL for the same architecture as whatever architecture R is built under (i.e. 64-bit if using 64-bit R).
Mac OSX
Follow the same procedure for Linux, just make sure that you install Xcode (which comes with a C/C++ compiler) and you might need to update Xcode if g++ --version is less than 4.1.0. If you are using an old version of Mac OSX (< 10.5), you might need to use an older version of the GSL.
Windows
It is highly recommended that you install a pre-compiled GSL in Windows. Compiling the GSL from source in Windows is at best tricky and at worst nightmarish. I use the Boost Science Package compiled by Gordon Taft:
C:\Boost_Science_library\ .Conclustion
Now you can try to install RBrownie. It should work and if it does not then post here and we will try to help you out.