  We give a proof of the Homotopy Transfer Theorem following Kadeishvili's
original strategy. Although Kadeishvili originally restricted himself to
transferring a dg algebra structure to an $A_\infty$-structure on homology, we
will see that a small modification of his argument proves the general case of
transferring any kind of $\infty$-algebra structure along a quasi-isomorphism,
under weaker hypotheses than existing proofs of this result.
