Austin gave jurisprudence its first rigorous attempt to say what law is without saying what it ought to be, and the theory was influential for a century largely because it was so clear about what it claimed.
The Province of Jurisprudence Determined (1832) sets out the command theory. A law is a command issued by a sovereign — a determinate person or body habitually obeyed by the bulk of a society and not habitually obedient to anyone else — and backed by the threat of an evil for disobedience. From this follow the boundaries he cared about: rules of positive morality, international law and constitutional convention are not law properly so called, because no sovereign commands them and no sanction enforces them.
The separation thesis is his enduring contribution, and he stated it with unusual bluntness: the existence of law is one thing, its merit or demerit another. A law which actually exists is a law, though we happen to dislike it. He was not indifferent to the difference — he was a Benthamite utilitarian who thought bad laws should be attacked — but held that a doctrine dissolving unjust rules out of the category of law leaves the reformer with nothing to reform.
His teaching career was a failure; the lectures were poorly attended and he resigned his London chair, and the book's reputation was made posthumously by his widow Sarah, who edited and republished it.
Hart's Concept of Law (1961) demolished the command theory so thoroughly that Austin is now read mainly through that critique: sanctions do not explain rules conferring powers, habitual obedience does not explain the continuity of authority, and the internal attitude of officials to a rule has no place in his scheme. The separation thesis survived the demolition intact.