[1] The book was based on a series of lectures Hilbert made in the winter of 1920–21.

"[2] It differentiates between two tendencies in mathematics and any other scientific research: on the one hand, toward abstraction and logical relations, correlating the subject matter in a systematic and orderly manner, and on the other hand an intuitive approach, which moves toward a more immediate grasp of and a "live rapport" with the same material.

Further he asserts that intuitive understanding actually plays a major role for the researcher as well as anyone who wishes to study and appreciate Geometry.

[3] Topics covered by the chapters in the book include the Leibniz formula for π, configurations of points and lines with equally many points on each line and equally many lines through each point, curvature and non-Euclidean geometry, mechanical linkages, the classification of manifolds by their Euler characteristic, and the four color theorem.

[4] Physics Today called it "a readable exposition of modern geometry and its relation to other branches of mathematics".