I find the so-called "cosmological argument" to be compelling and significant, as refuting both Platonic Realism and Materialism.

Aristotle's eudaimonism (i.e. virtue ethics), (syllogistic) logic and hylomorphism (i.e. immanent realism) have been very influential to my thinking.

"Compelling," "convincing," "hardest to argue against." Being a reader of some Aristotle, and finding it mainly difficult, I can't really use your words. Instead, persuasive and appreciation work for me. He's persuasive and I appreciative, both these necessary ingredients sine qua non. And what I do with them - on the basis of them - is buy. I buy his of virtue of mean and balance. Of logic. Of rhetoric. Of poetry and drama. Of happiness defined over a long life, although not entirely his list of particulars. Of four causes. In a sense these tools, and with a 2000+ year pedigree of efficacy. But as tools, not expected to work on what they are not intended for. And as good tools, admirable, good to hands-on, even when not in use.

And where he is wrong, if I can understand it, I appreciate how he is wrong, and how he is from his standpoint right.

* By Aristotelian philosophy I mean both the philosophy of Aristotle and of those who generally are considered to subscribe to Aristotle's system. — banana peel

I don't have a book reference -- I actually lost my collection of books, which I intend to replace once I get the time and motivation.

But the one thing that comes to mind is the essence of human being -- being rational is the essence of human being. So, Aristotle's essentialism is the one thing that's easily mentioned.

which part of Aristotelian philosophy convinces you the most or which one you find it the hardest to argue against. — banana peel

I believe there's essence in every entity -- what it is that necessarily belongs to an entity for its identity. The appleness of apple, for example.

In the Aristotelian scheme, nous is the basic understanding or awareness that allows human beings to think rationally. For Aristotle, this was distinct from the processing of sensory perception, including the use of imagination and memory, which other animals can do. This therefore connects discussion of nous to discussion of how the human mind sets definitions in a consistent and communicable way, and whether people must be born with some innate potential to understand the same universal categories in the same logical ways. Deriving from this it was also sometimes argued, especially in classical and medieval philosophy, that the individual nous must require help of a spiritual and divine type (a.k.a ‘illumination’). By this type of account, it came to be argued that the human understanding (nous) somehow stems from this cosmic nous, which is however not just a recipient of order, but a creator of it.