Since you mentioned complexity and Einstein, the following Einstein quote is mandatory:
Everything should be made as simple as possible, but not simpler

In hindsight, some things in Bitcoin could have been made more simple; for instance, the way how transaction signing is performed (which, BTW, leads to the current transaction malleability problem). This shows that, even though Satoshi can be called a genius, not even he is perfect.

If you want to become an expert, it doesn't hurt to be a programmer. If you have no programming experience, I think Python is a nice language to start with: it's relatively friendly to beginners, and it has everything experts want (except, arguably, speed, but often that's not critical). Then, you might want to check out my implementation of Bitcoin transaction algorithms in Python. Calculation of the transaction hash ( = transaction ID) is a single line of code in the getTransactionID method.