My wife uses the Amazon Kindle app on her Android tablet. You can use it for non-Kindle books by sending an email to a special email address for your Kindle account: www.amazon.com/sendtokindle/email.
Calibre is useful for this. It shows an easy to use “send to Kindle” button, and can convert books in ePub, mobi, etc formats to the format that works best in the Kindle app (AZW3).
If you want a web interface for Calibre (eg to run on a home server and download books when you’re away from your computer), Calibre-web works well.