I agree with Philip Wood, Faraday did not use high level mathematics to convey his findings.
He invented magnetic flux lines of force to explain what he discovered.
The facts are easy to state (Faraday's laws)
Whenever a conductor experiences a changing magnetic flux linkage and emf is induced.
The induced emf = rate of change of flux linkage
The emf opposes the changing flux linkage (usually known as Lenz's law)
The - sign in an equation indicates 'opposition' this occurs in other aspects of physics (SHM etc)
If there is a complete circuit the induced emf causes a (induced) current to flow.