Luis Santaló published in both English and Spanish:
Introduction to Integral Geometry (1953)
Chapter I. Metric integral geometry of the plane including densities and the
isoperimetric inequality. Ch. II. Integral geometry on surfaces including Blaschke's formula and the isoperimetric inequality on surfaces of constant curvature. Ch. III. General integral geometry: Lie groups
on the plane: central-affine, unimodular affine, projective groups.
Geometrias no Euclidianas (1961)
I. The Elements of Euclid
II. Non-Euclidean geometries
III., IV.
conics
V, VI, VII. Hyperbolic geometry: graphic properties, angles and distances, areas and curves.
(This text develops the
Klein model
, the earliest instance of a model.)
VIII. Other models of non-Euclidean geometry
Geometria proyectiva (1966)
A curious feature of this book on projective geometry is the opening on
quadrics. Serious and coordinated study of this text is invited by 240 exercises
at the end of 25 sections, with solutions on pages 347–65.
Integral Geometry and Geometric Probability (1976)[2]
Amplifies and extends the 1953 text.
For instance, in Chapter 19, he notes “Trends in Integral Geometry” and includes “The integral geometry of Gelfand” (p. 345) which involves inverting the Radon transform.
Santaló, Luis Antonio (2009), Naveira, Antonio M.; Reventós, Agustí; Birman, Graciela S.; et al. (eds.), Luis Antonio Santaló selected works, Berlin, New York:
