Open Source Web Project Management Software

OdooSuite of open-source business apps written in Python
OpenProjectCollaborative Project Management
WekanTrello-like Kanban
FocalboardSelf-hosted project management tool
TaigaWeb-based tool for agile project management
KanboardKanban board for small teams and individuals
tuleapImprove management of software development and collaboration
eGroupWareEnterprise ready web-based groupware suite with project management
RedmineFlexible application written using the Ruby on Rails framework
LibrePlanProject planning, monitoring and control
TracProject management and bug/issue tracking system
LeantimeProject management for the non-project manager
TaskBoardKanban-inspired app for keeping track of things
dotProjectWeb-based, multi-user, multi-language project management application