This new volume presents 15 papers treating discrete groups as they occur in areas such as algebra, analysis, geometry, number theory and topology. Most of the papers are surveys, and the volume is intended to help graduate students and researchers better understand the structures and applications of discrete subgroups of Lie groups and locally symmetric spaces. Discrete subgroups of Lie groups are foundational objects in modern mathematics and occur naturally in different subjects. This new volume presents 15 papers treating discrete groups as they occur in areas such as algebra, analysis, geometry, number theory, and topology. Most of the papers are surveys, and this volume is intended to help graduate students and researchers better understand the structures and applications of discrete subgroups of Lie groups and locally symmetric spaces.