1 Introduction

2 Elementary notions

3 Convex bodies

4 Lunes

5 Width and thickness of a convex body

6 Reduced spherical bodies

7 More about reduced bodies on \( S^2 \)

8 Spherical reduced polygons

9 Diameter of convex bodies and reduced bodies

10 Bodies of constant width

11 Complete spherical convex bodies

12 Final remarks