What mathematics do I need to study in order to understand fully homomorphic encryption? I am currently working on a project that requires me to use the HElib library that implements the BGV homomorphic encryption scheme described in this paper. I need to be able to tune the parameters correctly so I am trying to understand the underlying concepts. However, I find the mathematical notation in the paper quite complicated. Perhaps someone can suggest a set of mathematical concepts that I should study before reading the paper. 

Edit: I've just finished my third year in a computer science undergrad program. So my background includes basic courses on discrete math, linear algebra, probability and statistics, theory of computation..etc. I have self-studied some basics of cryptography such as AES, DES, RSA..etc.
Knowing more about your background, you will definitely want to brush up on some abstract algebra. The book I link to below is pretty popular and introductory. I think it's just at your level. Also, understanding concepts like groups, rings (see below), homomorphisms, and fields are useful in understanding modern crypto. You won't be wasting your time at all.



Probably the most important skill is that vague term known as mathematical maturity, part of which includes


  fearlessness in the face of symbols


Along with this is understanding how to read a mathematical proof.

You should know about provable security as well, in particular how a problem can be reduced to another, such as how the security of the lattice shortest vector problem (SVP) can be reduced to the security of RLWE.

You should be familiar with big-$O$ notation.

You should be familiar with probability distributions, in particular the uniform and Gaussian distributions, and what it means to sample from a distribution.

As mentioned in the comments, you need to learn some abstract algebra. Back in the day, I learned enough to start from Pinter's A Book of Abstract Algebra. It has some very gentle prerequisites. You'll definitely need to learn about rings and quotient rings (RLWE means "ring learning with errors").

You'll need some linear algebra (especially norms and inner products) and lattices.

You'll need some algebraic number theory (see section 5.1.1).

Now, this is a lot, and I don't know if you just want to "get the gist" of the paper or hopefully start contributing original research. But again, "mathematical maturity", or trying to cultivate it, is the most important thing regardless!