At first glance, very unsimilar are 而 and 与. But, their functions in a sentence (at least when 而 is not 汝 and 与 is not 与える) are very similar to each other.
In short, they connect bits and pieces together to form a coherent thought. The main thing to keep in mind is that 而 connects verbs and clauses together (much like して～) and 与 connects nouns together (と).
For example, the 而 in 学而時習之 connects 学 and, strictly speaking, 習. Whereas,
知与不知 （知ると知らざると) connects two nouns together. Wait, aren’t those two verbs? Well, not quite. I believe I’ve mentioned it before, but nouns are often removed as superfluous in both classical Chinese and classical Japanese (thus giving rise to such things like これやこの行くも帰るも別れては知るも知らぬも逢坂の関). In other words, 知っている人と知らない人と.
I shouldn’t have to say this, but there are, of course, exceptions. But, in this case, thankfully, they are rare and not worth mentioning. So, with that, I will end this uncharacteristically short.