In my department, the core principles are described as follows. Consumer preferences are derived from indifference curves, and from theese curves the consumer demand curves are formed. Supply stems from production isoquants and the three stages of production, which yields supply curves. Putting the two together, you have supply and demand, from which the instructor should spend considerable time covers substitutes, complements, normal goods, inferior goods, and elasticities.
I don't like this view. You could learn all this and really know nothing about economics. Consumer indifference curves are useful for some problems, but are not the foundation of consumer demand. To get demand curves from these indifference curves, one must make assumptions about their shape to avoid giffin goods, which implies they are not the foundation of demand curves--demand curves are entirely an empirical construction. Now for production. One of my colleagues once stated that the stages of production are of paramount importance, because a falling marginal product curve drives everything. Yet what does it "drive?" All it does is imply that prices are positive but not infinite, and that we consume a finite amount of any good. If that is all the production stages can do, that is not impressive. Topics like substitutes and normal goods and elasticities are good for writing exam questions, but alone do not answer any economic questions.
So what are the "core principles" of economics? Frankly, I don't believe there is a general model of economics that encompasses everything. To me, the most important concept is the indifference principle. Which does not turn up in a Google search, nor is any any textbook except my own. More on the indifference principle later.