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When you take the Attack action and make a weapon attack with one hand using a weapon with the light property or a special attack (like a grapple or shove), as a bonus action you can make one additional weapon attack using a weapon with the light property that you're wielding in the other hand. You don't add your ability modifier to the damage of the additional attack, unless that modifier is negative.
Improvement to the Extra Attack (2) / (3) feature
If you have the Extra Attack feature and with it you can make three or four attacks with the Attack action, when you engage in Two-Weapon Fighting you can make two additional weapon attacks instead of one. In addition, when you make an opportunity attack or an attack with the Ready action, you can engage in Two-Weapon Fighting, but you can only make one additional attack.