For compilation of the LaTeX source, you need a full TeX Live installation, as well as SageMath (used to generate some plots). To run the Sage code, you just need SageMath.
These packages can be installed on Ubuntu 16.04 as follows.
sudo apt install texlive-full sagemath
To compile the LaTeX, just run make -C latex, which should generate latex/ecc.pdf. Run make -C clean to remove all generated artifacts. A precompiled ecc.pdf has been included in the repository root for convenience.
To do a simple test of the Sage code, run make -C sage. For your own tests, just load the relevant files in a Sage environment (see the sage/test.sage file for an example).