This, the Twenty-Seventh Yearbook, and its companion volume, the Twenty-Eighth Yearbook, have been long in the making. Into these two books have gone the combined contributions, suggestions, and criticisms of innumerable individuals, committees, and subcommittees. The academically talented student in mathematics has always been with us, and most teachers have always attempted to provide for his special needs in one way or another. The principal purpose of this year-book is to give teachers one more resource in order to provide for the talented more efficiently and more quickly. .