All 4 Uses

nevertheless
in
The Iliad by Homer (translated by: Lang, Leaf, & Myers)
(Auto-generated)

Therefore do I not marvel that the Achaians should fret beside their beaked ships; yet nevertheless is it shameful to wait long and to depart empty.†
Book 2 *

nevertheless = despite that (used to connect contrasting ideas)
Nevertheless will I tell thee wherefore I called thee hither.†
Book 24
Nevertheless hath some god stretched forth his hand even over me in that he hath sent a wayfarer such as thou to meet me, a bearer of good luck, by the nobleness of thy form and semblance; and thou art wise of heart and of blessed parents art thou sprung.†
Book 24
Nevertheless while he heareth of thee as yet alive he rejoiceth in his heart, and hopeth withal day after day that he shall see his dear son returning from Troy-land.†
Book 24

Definitions:

(1) (nevertheless)
despite that

Based on idea 1 we might not expect idea 2, but this is a way of saying that even though idea 1 was just stated, we still have idea 2. Synonyms include in spite of that, despite that, nevertheless, nonetheless, on the other hand, in contrast and but.
(2) (meaning too rare to warrant focus)