F-Droid (https://f-droid.org/ ) (GPLv3+) – libre software repository browser, from which the following can be downloaded (To install, you need to enable ‘unknown sources’ because it is independent to Google.);
• F-Droid 0.102.3 is the last version of the repository browser application to feature the Android Holo UI, but has been moved to F-Droid.org's ‘archive’ repository and is now quite difficult to find, so here is a direct link to its APK (Android installation PacKage): https://f-droid.org/archive/org.fdroid.fdroid_102350.apk (tip: instead of browsing ‘What's New’, which is typically experimental, select ‘Recently Updated’, which includes mature applications);

FAST App Search Tool (GPLv3) – quick application launcher from double-clicking or up-swiping the home button;

Hanger (GPLv3) – recent application launcher widget for notification bar (tip: pin FAST so that you can quickly get to applications that have fallen off the list);

Kiwix (GPLv3) – offline Wikibooks, Wiktionary, Wikipedia, Gutenburg, etc.;

LibreTorrent (GPLv3) – reliably download large files such as those used by Kiwix;

RPN (GPLv3+) – step-by-step calculator with no need for parentheses (e.g. try pressing [[1]], [[Enter]], [[2]], [[Enter]], [[3]], [[×]], [[+]] and compare this with [[1]], [[Enter]], [[2]], [[+]], [[3]], [[×]]);

Open Camera (GPLv3+) – advanced still and video camera;

MuPDF (AGPLv3+) – view portable documents (PDFs) often attached to emails or downloaded;

VLC (GPLv3) – media player;

LeafPic (GPLv3) – media gallery;

Hashr (GPLv3+) – verify files;

Amaze (GPLv3) – file manager;

Ghost Commander (GPLv3) – advanced file manager;

Turbo Editor (GPLv3+) – text editor;

Lock Screen (GPLv3+) – in combination with unchecking the ‘Power button instantly locks’ security setting, this is a partial workaround for Android not distinguishing between locking the screen and locking for security;

SatStat (GPLv3+) – sensor status with ability to manually or automatically update AGPS data for quicker positioning fix;

Transportr (GPLv3+) – public transport planner;

Suntimes (GPLv3+) – show, and set alarms for, sunset, twilight times, sunrise, and noon;

React (GPLv3+) – test your reaction time;

Periodic Table (GPLv3) – chemical element browser;

Quill (GPLv3) – draw visual notes, especially with stylus (lacks handwriting recognition);

Flym (GPLv3) – feed reader, supports RSS and Atom feeds;

WiFi Analyzer (GPLv3) – analyses Wi-Fi channels;

Rotation Manager (GPLv3) – set application-specific orientations, a workaround for some Android rotation issues;

OsmAnd (GPLv3) – offline OpenStreetMap;

NewPipe (GPLv3+) – YouTube downloader for later offline playing;

Mitzuli (GPLv2+) – offline translator;

Barcode Scanner (Apache2) – scan barcodes and share via QR codes;

K-9 Mail (Apache2) – email client;

LibreOffice Viewer (MPLv2) – view office documents;

IceCat Mobile (MPLv2) – Web browser;

Activity Launcher (ISC) – create homescreen shortcuts directly to specific activities within applications, such as the ‘Tethering & portable hotspot’ activity within Settings.