Cal.com is an open-source alternative to Calendy for scheduling meetings

Meeting invites showing one image of an e-mail format invite to someone giving various optional times to choose from. On the right side is an app open on a phone, prompting the user to just pick a time that works best from them from a month calendar view.

Cal.com works by everyone sharing their calendars to it, and it then suggests times when everyone should be available. It is great for doctors, dentists, teachers, companies meeting candidates, etc who need to set up meetings and want the process as automated as possible.

It can be self-hosted for complete privacy, or they also offer a hosted service which is free for individuals. Not only that, but it can connect to many types of calendaring services, and also has support for CalDav.

See https://cal.com/