Open-source alternatives to Linear

Plane is open source: free to download and run on your own server. Linear costs from $10 a month, with a free plan.

Plane

Open source (AGPL-3.0) · Open-source project management for issues, cycles and roadmaps

Plane tracks issues, runs cycles (sprints) and manages product roadmaps. Use Plane Cloud or install it on your own servers.

Free to download and run on your own server under the AGPL-3.0 licence; you pay only for your hosting. Plane Cloud has a free account.

Free to use, not free to run. The licence costs nothing, but self-hosting needs a server (often $5 to $40 a month) and someone to install updates and keep backups.
Open core means the main product is open source but some features, usually for larger teams, need a paid licence.
Hosted versions exist for many of these, run by the makers. They cost money but save the upkeep, and you can still move to your own server later.
Licences differ. MIT and Apache allow almost anything. GPL and AGPL require you to share changes you make to the code; for normal business use, that rarely matters.