This is a list of Alternative and Open Source Android Apps and OS I could recommend because I use most of them since November 2013 under Paranoid Android with a Nexus 5.
Most of these apps are available via F-Droid.
And when alternative don't exist and/or it not available via F-Droid, Aptoide and/or anothers repos; I use https://apps.evozi.com/apk-downloader/ to extract the apk from Google Play.
A free and open source podcastmanager for Android, allowing you to subscribe to podcasts (via iTunes database & OPML), automatically download episodes using powerful mechanisms and listen to them the way you like (speed, balance adjustments, etc).
A podcast manager allowing you to subscribe and download automatically your favorite podcasts.
An virtual keyboard who don't save your keystrokes.
AOKP stands for Android Open Kang Project. It is a custom ROM distribution for many Android devices. It is mostly based off of AOSP.
If you're serious about degooglelising you're phone than replace the ROM.
BARIA stands for "Backup And Restore Installed Apps." Are you a person trying different ROMs on your mobile phone OR resetting phone for better performance ?.
To make offline backup of your apps.
Scan barcodes on CDs, books, and other products, then look up prices and reviews, or search for a word in a book and find where it occurs. You can also scan QR Codes containing URLs, contact info, calendar events, and more.
Because human don't read QR and BarCode.
Cache Cleaner is an ad-free open source tool for cache cleaning which does not require rooted device. Features native Holo look and feel and fast operation.
In case you need to clean your droid.
Sync you're calendar, contacts and notes with your cloud.
DiskUsage provides a way to find out which files and directories on the SD card of your Android phone are consuming the most space. It displays diagram with directories/subdirectories proportional to their size. Users are allowed to zoom in to look at specific directory content.
Document Viewer is a highly customizable document viewer for Android, fork of the last GPL version of 
EBookDroid .
A good start to degooglelising you're apps and android is to replace the Google Play store.
Ghost Commander is a file manager with two panels for the Android™ platform. Its development was inspired by the famous (Norton|Midnight|Total) Commander desktop applications, so if you are familiar with those great programs, you will find Ghost Commander a familiar and very...
Nnavigate FTP, SFTP, SMB and Media Storage.
FreeOTP is a two-factor authentication application for systems utilizing one-time password protocols with support for Android (6 or later) and iOS (11 or later). Tokens can be added easily by scanning a QR-code or by manually entering in the token configuration.
One Time Password manager to replace Google Authenticator.
K-9 is an open source email client for Android with multi-folder sync, email signatures, Bcc-to-self, return-address configuration, keyboard shortcuts, Exchange Support, message flagging, IMAP deletes, saving attachments, configurable notifications and more.
Android password manager supporting KeePass 1.x and 2.x formats, without needing internet permission for added safety.
A usefull when you password database apps.
Kimai is a free open source time tracker. It tracks work time and prints out a summary of your activities on demand. Yearly, monthly, daily, by customer, by project, by action …
Open-source browser with Gecko engine, supporting HTML add-ons and providing privacy features like Enhanced Tracking Protection and third-party cookie blocking.
On-premises file sync, universal access, integrated collaboration, real-time communication with privacy and data control focus.
Help you to sync your data, calendar, contact and note like we do with Google Cloud and Apple iCloud.
Distraction-free note-taking app with categories, Markdown formatting, favorites, and RESTful API. Integrates with Nextcloud clients for seamless syncing.
To sync your notes in the our cloud.
Lightweight and open-source app for YouTube, PeerTube, SoundCloud, and more. No Google Account needed, supports 4K and background audio streaming with downloads.
Paranoid Android provides a unique experience and ultimate customization for your Android device.
If you're serious about degooglelising you're phone than replace the ROM.
A simple FTP server. Allows to exchange files with other machines over wifi. No more USB cable searching. Runs without root privileges. Is not started when device boots (but can if you wish). Control yourself when the server runs.
If you need a FTP Server on your phone, this is the apps you need.
Listen streaming radio
Helps access and share practical educational content on digital security. This app exists as a part of a digital platform which will provide essential digital security information.
Do you want to share the links you discover? Shaarli is a minimalist delicious clone that you can install on your own server. It is designed to be personal (single-user), fast and handy.
Protect your communication in transit and on your phone. Silence (formerly SMSSecure) is a full replacement for the default text messaging application: all messages are encrypted locally and messages to other Silence users are encrypted over the air.
Experience instant messaging with remarkable speed and robust security. Join massive group chats or channels. Enjoy free and advanced features.
TTRSS-Reader is a client application for the project 
Tiny Tiny RSS , a PHP-based online feedreader which runs on your own webspace. If you want to host your own feedreader, want a cross-device-solution and don't want to use...
Cross-platform, free media player supports multimedia files, DVDs, streaming, offers hardware acceleration, 4K, lossless audio, and more.
VyprVPN is a fast and secure way to browse the web. VyprVPN replaces your real IP address with an IP address from one of their many worldwide VPN server clusters protecting your privacy while online.
Open-source, self-hosted tool that extracts articles, offers offline mobile reading, powerful filters, migration from other services, and multiple download formats.
Wifi Analyzer is a handy tool which helps you to select a better channel for your wireless router. It turns you android phone into a handy Wi-Fi analyzer!
Zoiper IAX & SIP multilanguage and multiplatform (Windows, Linux and Mac OS X) softphone is a VoIP soft client, meant to work with any IP-based communications systems and infrastructure.
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