Open-source Application lifecycle management tools (ALM) are many and can vary very much. These are just comparison of some of the best vendors:
1.MyCollab is a multi-purpose solution which features tools for customer relationship management, document management, and project management. In this case, let's look at MyCollab-Project.
MyCollab-Project includes many features, like a Gantt chart and milestones, time tracking, and issue management. It also supports agile development models with its Kanban board. MyCollab-Project comes in three editions, of which the community edition is the free and open source option.
2. Odoo is a full suite of business applications, of which project management is just one. Odoo is a multiplatform solution, supporting Windows, several Linux distributions, and other operating systems as well.
The community edition is, of course, free and open source, but limited in features compared to the enterprise version. Odoo project management has some interesting features, such as Gantt charts, a Kanban view, tasks and issues, graphs, and more.
3. Taiga is an open source project management platform for startups, agile developers, and designers. It focuses on agile development methods, and has all of the required features such as a backlog, Kanban board, tasks, sprints, and issues.
Notable pros are the integration with GitHub, GitLab, and Bitbucket, making it an interesting project management tool for developers. Taiga can also be extended through plugins, and has a REST API.
4. OrangeScrum is a project management tool for freelancers, agencies, and small to medium businesses. It includes features such as a scrum task board, resource planning, progress tracking, Kanban and Gantt chart views.
5. With a focus on software development projects, Tuleap provides a feature rich platform which includes project management features like Scrum and Kanban support, tracking, document management, and other collaborative tools.
Pros for Tuleap are support for agile, traditional, hybrid, or custom processes for project management. It supports planning, sprints, tasks, reports, and more. This tool is very suitable for open source development companies, as the tool also integrates with Git, SVN, Jenkins, and more. Tuleap also provides an appliance installation (virtual machine), or installation through Ansible.