Last Saturday we had some problems with understanding names of departments in an American / European company. I think that the first step to understand them is to know the Japanese translation. But it is important to know also its meaning. I suggest starting with wikipedia:
marketing = マーケティング Please check also here.
advertising = 業界 (koukokugyoukai)
research = 研究 (kenkyuu)
Research and Development = 研究開発 Please check also here.
Human Resources = 人事 (jinji) Please check also here.
While researching the above terms, I came across an online dictionary with word lists grouped in categories – looks very useful!