Overview

This collection of expository articles by a range of established experts and newer researchers provides an overview of the recent developments in the theory of locally compact groups. It includes introductory articles on totally disconnected locally compact groups, profinite groups, p-adic Lie groups and the metric geometry of locally compact groups.

Concrete Examples

Concrete examples, including groups acting on trees and Neretin groups, are discussed in detail.

Structure Theory

An outline of the emerging structure theory of locally compact groups beyond the connected case is presented through three complementary approaches: Willis's theory of the scale function, global decompositions by means of subnormal series, and the local approach relying on the structure lattice.

Additional Topics

An introduction to lattices, invariant random subgroups and L²-invariants, and a brief account of the Burger–Mozes construction of simple lattices are also included.

Future Research

A final chapter collects various problems suggesting future research directions.