1. John Austin (command theory / analytical positivism)
"A law is a command which obliges a person or persons to a course of conduct."
For Austin, every law is (i) a command of a determinate sovereign, (ii) imposing a duty, and (iii) backed by a sanction. Law is "the science of what is," not "what ought to be" — the lawyer studies law as it is enacted, regardless of its morality.
Criticism: It cannot explain laws that confer rights without duties (contract, wills, marriage laws), customary law, international law, or laws limiting the law-maker itself (constitutions). As Prof. Hart showed in The Concept of Law (1961), a legal system is not a gunman's writ large: it is a union of primary rules (duties) and secondary rules (rules about making, changing and adjudicating rules).
2. John Salmond
"Law is the body of principles recognised and applied by the State in the administration of justice."
Salmond's emphasis is on the courts: law is what the courts recognise and enforce. Criticism: it ignores the legislature as a source of law and reduces law to case-law.
3. T. E. Holland
"Law is a general rule of external human action enforced by a sovereign political authority."
Holland calls jurisprudence "the formal science of positive law" — he is interested only in the form of law, not its content. Criticism: like Austin, "general rule" excludes special laws, and "sovereign" sits uneasily with modern constitutionalism.
4. Sir William Blackstone
Municipal law is "a rule of civil conduct prescribed by the supreme power in a State, commanding what is right and prohibiting what is wrong."
5. Frederick Pollock (refining Austin)
"Law is a general rule of external human action enforced by the determinate authority."
6. Roscoe Pound (sociological approach)
"Law is the body of principles, standards and rules which the courts apply in the administration of justice" — more generally, law is social engineering: the balancing of competing interests in society.
7. Historical school — F. K. von Savigny
Law is not made arbitrarily; it grows out of the Volksgeist — the spirit/common consciousness of the people. Custom, not command, is the primary form of law.
8. H. L. A. Hart (modern positivism)
Law is the union of primary rules (imposing duties) and secondary rules (rules of recognition, change and adjudication). Hart's work remains the modern starting point of positivist theory.