Aimed toward graduate students and research mathematicians, with minimal prerequisites this book provides a fresh take on Alexandrov geometry and explains the importance of CAT(0) geometry in geometric group theory. Beginning with an overview of fundamentals, definitions, and conventions, this book quickly moves forward to discuss the Reshetnyak gluing theorem and applies it to the billiards problems. The HadamardCartan globalization theorem is explored and applied to construct exotic aspherical manifolds.

Explains the importance of CAT(0) geometry in geometric group theory Demonstrates Alexandrov geometry through applications and theorems Discusses Reshetnyak gluing theorem and Hadamard-Cartan globilization theorem

Inhalt
1 Preliminaries.- 2 Gluing theorem and billiards.- 3 Globalization and asphericity.- 4 Subsets.- 5 Semisolutions.