This document offers a list of mathematical periodicals which has been prepared for the use of research students in mathematics in the universities of the United States. The selection has been made after consultation with a number of professors in those universities that have most to do with directing research work in mathematics in this country, and it represents the periodicals which, in the judgment of these advisers, the student will be most apt to consult in his investigations. The present list is divided into two parts. In the first part those periodicals appear which relate solely to mathematics, whether they are issued in the form of journals or of publications of scientific societies. The second part includes those periodicals which contain mathematical articles which the student will probably wish to consult, but which are not wholly concerned with such articles. The index permits the student to refer at once to each list and also to find with ease the periodical for which he is looking under any one of various names by which it is known, or under the place of its publication. [Best copy available has been provided.].