What's a good term/phrase for things of a specific branch everybody should know?

Essentials is a good word for this:

basic, indispensable, or necessary elements

The basics is a similar term:

something that is fundamental or basic; an essential ingredient, principle, procedure, etc.: to learn the basics of music

Fundamentals would sound well in a scientific context:

a basic principle, rule, law, or the like, that serves as the groundwork of a system; essential part: to master the fundamentals of a trade.

A high register, rarer term is

requisites

Prerequisites are what you need to now before you study something; the requisites are what you need to know for the thing of study.

Principles would be one of the most potential terms helpful in search.

Also, you can think of all the book titles beginning with 'Principles of...', 'Elements of...', 'Fundamentals of...', etc., which is actually the reason they are so titled.