There are a few calendar apps available in the app store, including BookThatApp: https://apps.shopify.com/bookthatapp
We have a large number of merchants using it to manage class bookings. The App adds a calendar to your online store that displays your classes (or courses), allows customers to log in and see what classes have been booked, and can send reminder notifications just before the class starts. Adding, updating and deleting class times is done in the app's admin.
Please feel to email us at email@example.com if you have any questions or need help setting it up.