What subject did the Buddha teach?

The best way of answering this is to quote the Buddha himself;"Known this;O'Monkks: Now; as formerly; I teach of only dukkha (suffering; unsatisfactoriness) and the elimination of dukkha".
Whether or not this answer agree with what you had thought; please take good note of it.There are many other ways we may answer; but this one saying of the Buddha sums up his teaching very succinctly.
The Buddha taught only dukkha and the quenching of it. This renders irrelevant any questions without adirect bearing on the elimination of dukkha.Don't consider such questions as " Is there rebirth? "or" How does rebirth take place?" These can be considered later.
So; if a Westerner asks us this question; we shall answer it by saying; "The Buddha taught nothing other than dukkha and the elimination of it.
As YOU CAN see; this is a big subject which can be answered from many different points of view. If asked this ; we can say first of all that he taught us to tread the Middle Way; to be neither too strict nor too slack; to go to neither the one extreme nor the other.
On the one hand; we are to avoid the very harsh self-mortification practised in certain yoga schools; which simply creates difficulties and trouble. On the other hand ; we must keep away from that way of practice which allows us sensual pleasures; which amounts to saying ; " Eat ; drink; and be merry ; for tomorrow we die!"
This is an extremely cynical expression appropriate for people interested only insensual pleasures. By contrast; the Middle way consists; on one hand; not indulging to your hearts content in sensual pleasures.
Walking the middle way brings about conditions which are in putting an end to study and practice ; and to success in putting an end to dukkha ( suffering) . The expression "Middle Way" can be applied generally in many varied situations. It can't lead you astray.
The middle way consists in striking the golden mean. Knowing causes; knowing effects; knowing oneself; knowing how much is enough; knowing the proper time; knowing individuals; knowing group of people: these Seven Noble Virtues constitude walking the Middle Way. This one way of answering the question.

Credit : Dr. Variably Ccu Mu Da.