You don't really need a book. Here's how it breaks down.
When an investor invests, he or she is buying a portion of a company. Say I invest $100,000 at a $1 million valuation - I'm actually buying 10% of the company (since 100k is 10% of 1M). There's technically pre-money valuation and post-money valuation, so the company was worth $900K pre and $1M post (depending on whether or not you're including the investor's money in the valuation), but we'll assume we mean post-money valuation for now.
A "convertible note" is someone saying "OK, I'll give you 10k now, we'll call it 'debt' the company owes me because the law makes us call it something, but once you raise your round that 'debt' will 'convert' to equity at whatever terms you set with other investors." Really it's just a relatively fast and easy way to say "Here's 10k, I'll take whatever terms you set with the next round of investors." Almost like a bit of a fundraising hack because the legal fees and time of the negotiations just aren't worth it. Sometimes convertible notes have a cap (i.e. a maximum valuation - if you go over that valuation you grant equity as if it were really a lower valuation) or a discount (i.e. I'm investing at whatever valuation the other investors set minus 20%). It just depends on what the structure of the investment is. Long story short: a convertible note is a quick investment that isn't worth much until the company raises its next round.
The SAFE is basically YC's response to a convertible note, because the convertible note carries some side effects that nobody wanted and are a bit ridiculous. There are some things that technically happen with debt, (interest, some regulations) that nobody involved actually wanted, but were a legal byproduct of calling something "debt." A SAFE is more honest, and says "Hey, we're buying a portion of the company, just not yet" - hence the name Simple Agreement for Future Equity). A SAFE is similar to a convertible note in that it has options like caps and discounts, but it's basically what a convertible note should be were we not using the whole "debt" thing as a hack.
So with regard to YC and the "new deal": YC before was basically saying, "We'll give you 20k for 7% of the company, and then an extra 80k at whatever valuation you raise your next round so that you get it now instead of later." Now YC is saying, "We'll just give you 120k for 7% of the company."