In this book Professor Birkhoff presents his notable quantitative approach to various aesthetic fields—polygonal forms, ornaments and tilings, vases, harmony, melody, and the musical quality in poetry. His fundamental thesis is that the aesthetic measure depends upon the density of the elements of order in the aesthetic object. A psychological justification of the thesis is made at the outset, and in a later chapter is shown to be a natural outgrowth of earlier theories. The many illustrations, four of them in color, have been carefully chosen and will prove of much interest in themselves. The novelty and the systematic character of Professor Birkhoff’s theory will attract the attention of every student of the Fine Arts or aesthetics.