  We show how the existence of various free vector lattices and free vector
lattice algebras can be derived from a theorem on equational classes in
universal algebra. A discussion about free $f$-algebras over non-empty sets is
given, where the main issues appear to be open. It is indicated how the
existence results for free vector lattices and vector lattice algebras can be
used for easy proofs of existence results for free Banach lattices and free
Banach lattice algebras. A detailed exposition of the necessary material from
universal algebra is included.
