These three volumes constitute the first complete English translation of Felix Klein's seminal
series Elementarmathematik vom höheren Standpunkte aus. Complete has a twofold meaning here:
First there now exists a translation of volume III into English while until today the only
translation had been into Chinese. Second the English versions of volume I and II had omitted
several even extended parts of the original while we now present a complete revised
translation into modern English. The volumes first published between 1902 and 1908 are
lecture notes of courses that Klein offered to future mathematics teachers realizing a new
form of teacher training that remained valid and effective until today: Klein leads the
students to gain a more comprehensive and methodological point of view on school mathematics.
The volumes enable us to understand Klein's far-reaching conception of elementarisation of the
elementary from a higher standpoint in its implementation for school mathematics. This volume
II presents a paradigmatic realisation of Klein's approach of elementarisation for teacher
education. It is shown how the various geometries elaborated particularly since the beginning
of the 19th century are revealed as becoming unified in a new restructured geometry. As Klein
liked to stress: Projective geometry is all geometry. Non-Euclidean geometry proves to
constitute a part of this unifying process. The teaching of geometry is discussed in a separate
chapter which provides moreover important information on the history of geometry teaching and
an international comparison.
