Valve has a few reasons why Half-Life 2: Episode 3 never happened

Valve has explained why we never got Half-Life 2: Episode 3.

What to expect from Half Life 2: Episode 3/Half Life 3

Some Levels from Half-Life 2: Episode 3 Released

Half-Life 3 – the game that doesn't exist, Games

If everybody wants a Half-Life 3 game, what's preventing it from actually being made? - Quora

Half Life 2 Episode One PC : Video Games

Here Is Every Mod That Attempts To Make Half-Life 2: Episode Three feature - ModDB

Half-Life' Fans Look For Closure In Former Valve Writer's Apparent Outline For 'Episode 3

Valve, seriously, where is Half-Life 3?

15 Reasons Why We May NEVER See Half Life 3 Or Half Life 2: Episode 3