Open Source Booking System
A booking system is really a concurrency problem wearing a calendar: the entire job is preventing two people from grabbing the same slot while still showing real-time availability across staff, rooms, or resources. The open source options here run that scheduling engine on your own server, syncing with external calendars and handling time zones, buffers, and reminders, so the appointment data and your customers' contact details stay with you instead of a scheduling vendor.

Cal.diy
Self-hosted scheduling platform for individuals and self-hosters, the community edition of Cal.com

QloApps
Open-source hotel reservation system with a PMS, booking engine, and hotel website

Rallly
Open-source meeting poll tool for finding a date and time that works for the whole group

Easy!Appointments
Self-hosted appointment scheduler with customer management and Google Calendar sync

TastyIgniter
Open-source online ordering and table reservation system for restaurants and takeaways

LibreBooking
Open-source resource scheduling for reservations, waitlists, quotas, and usage reporting

classroombookings
Open-source room booking system for schools with self-hosted and hosted options

GYM One
Open source web software for managing gym members, classes, tickets, payments, and access control