DAVx⁵ is an open-source CalDAV/CardDAV suite and sync app for Android. You can also access your online files (WebDAV) with it.

DAVx⁵ manual

Nextcloud extension to support WebDAV-Push on calendars/address books

ICSx⁵ is an Android app to subscribe to remote or local iCalendar files (like time tables of your school/university or event files of your sports team).

WebDAV (including CalDAV, CardDAV) library for the Java virtual machine (Java/Kotlin)

Allows usage of iCalendar files with the Android calendar provider

WebDAV Push: Draft

Allows usage of vCard resources with the Android contacts provider

Android service + TrustManager for managing custom certificates in an app-private key store

ICSx⁵ Website