Concept: Library associations are professional bodies established to promote standards, research, training and professional development in library and information science.
Step 1: Match American Association of Law Libraries.
American Association of Law Libraries was established in 1906.
\[
A \rightarrow IV
\]
Step 2: Match American Society for Information Science and Technology.
American Society for Information Science and Technology is associated with 1937.
\[
B \rightarrow I
\]
Step 3: Match Association of Research Libraries.
Association of Research Libraries was established in 1932.
\[
C \rightarrow III
\]
Step 4: Match Medical Library Association.
The Medical Library Association was established in 1898.
\[
D \rightarrow II
\]
Therefore, the correct matching is:
\[
A-IV,\ B-I,\ C-III,\ D-II
\]