What is the difference between `nevertheless’ and `however’?

As far as the meaning is concerned, there is not much of a difference. The two can be used interchangeably in many contexts; `nevertheless’ is considered to be more formal than `however’. Both words are used when you wish to emphasise that the second point you are making contrasts with the first.

*He was very ugly to look at. However/nevertheless most girls wanted to marry him.

Source: The Hindu ‘Know Your English’ Series, January 2, 2006.