Further should be used when extending your point from a previous argument already made. Furthermore should be used when you’re introducing a new argument. Further is used in the middle of a sentence, while furthermore is used at the start of a sentence.

I had enough money to invest. I realized, further, that the risk was small. The police have been reluctant to take their investigation any further. I've never been further west than St. Louis.

Definition of Further to promote or advance forward Examples of Further in a sentence As a way to further her career, the manager took business classes at the local night school. The teacher tried to further the students’ understanding of the material by giving them extra help with difficult problems.