Step 1: Understanding the Concept:
The question asks to identify the seminal work of the influential 20th-century legal philosopher, H.L.A. Hart. Hart was a key figure in the school of legal positivism and his work profoundly shaped modern legal theory.
Step 2: Detailed Explanation:
\begin{itemize}
\item H.L.A. Hart (1907-1992): An English legal philosopher and a leading figure in analytical jurisprudence. His most famous and influential work is "The Concept of Law," first published in 1961.
\item In this book, Hart developed a sophisticated theory of legal positivism. He famously argued that law is a system of rules, comprising a union of "primary rules" (which impose duties) and "secondary rules" (which confer powers, such as rules of recognition, change, and adjudication). This work critiqued earlier positivist theories (like Austin's command theory) and engaged with natural law theories.
\item The other books mentioned are associated with other authors. For instance, "The Province of Jurisprudence Determined" is by John Austin, and "The Province and Function of Law" is by Julius Stone.
\end{itemize}
Step 3: Final Answer:
H. L. A. Hart's name is associated with the book The Concept of Law.