SQLite is a relational database management system and the most used database engine in the world.
Its a very small library, depending on which platform you use it can be only 600kb big. It is embedded into your application and runs there locally, meaning there is no server needed.
All you need to do is to create an SQLite database in your application and then you are able to use SQL to access and change the data. The database file is stored in your project. The SQLite library is already part of Android Studio so you can have a head start.
I found an example project for Android Studio online, which shows how you can use SQLite inside your Android app, this is the link:
You find the database file of this project like this: run your virtual device or connect the phone and run your app. Click on view→tool windows→ device file explorer. Then go to the folder data/data/info.androidhive.sqlite/databases.
Which databases are your favorites?