Universal Algebra is interesting because it shows that the meta-theory of many algebras is in some very formal sense uniform, leading to precise theorems.
But there is another part to Universal Algebra, always present in all expositions, but that gets less light: the many constructions it enables. For example, what a homomorphism is, and what a term algebra is, is a construction, not something that merely exists via some classical reasoning (i.e. using choice or excluded middle). There are, it turns out, many constructions.
What I'm looking for is a list of these, that both names them and defines them carefully. [The reason this can't easily be found in most textbooks is obvious: that is an eminently non-pedagogical mode of presentation. Such a list is an act of classification, not pedagogy. Of course, it is also ironic that this isn't the case, since Universal Algebra itself is a giant act of classification!]
Of course, I would be even happier to see constructions that work in multi-sorted quasi-equational algebras. But that part might actually be for MathOverflow.