Petrunin A. PIGTIKAL (puzzles in geometry that I know and love) 2022

Textbook in PDF format

The genre of this book is unusual: it is a collection of carefully selected problems in modern geometry, each having an elegant solution, usually based on a single non-trivial idea. The problems are supplied with sketches of solutions (called “semisolutions”) and comprehensive references to the literature: the bibliography comprises about 300 items. Arguably, many of these solutions qualify for “The Book”. The choice of the problems reflects the mathematical taste of the author and his research interests, that are quite broad. Many problems were suggested by users of MathOverflow, and the book is a perfect representative of the spirit of this network.
As the author says, “I am collecting these problems for fun, but they might be used to improve problem-solving skills in geometry.”
Curves.
Surfaces.
Comparison geometry.
Curvature free differential geometry.
Metric geometry.
Actions and coverings.
Topology.
Piecewise linear geometry.
Discrete geometry