Natural Armor. Your armor class is equal to 13 + your Constitution modifier. You are able to use shields and still benefit from this feature.
Powerful Build You count as one size larger when determining your carrying capacity and the weight you can push, drag, or lift.

Shell Defense. You can withdraw into your shell as an action. Until you emerge, you gain a +4 bonus to AC, and you have advantage on Strength and Constitution saving throws. While in your shell, you are prone, your speed is 0 and can't increase, you have disadvantage on Dexterity saving throws, you can't take reactions, and the only action you can take is a bonus action to emerge from your shell.

Shell Deflection. Whenever you take damage, you can use your reaction to reduce the damage take by your 1d12 + your Constitution modifier. Upon using this feature, you cannot do so again until you finish a short or long rest.

Brutal Shell. Whenever you use your Shell Deflection, you can make an unarmed strike using your shell against a creature within 5ft. of you. Upon a hit, you can deal additional damage equal to your level.
Jagged Claws Your claws are natural weapons, which you can use to make unarmed strikes. If you hit with them, you deal slashing damage equal to 1d6 + your Strength modifier, instead of the bludgeoning damage normal for an unarmed strike.

Spiny Defense. While in your Shell defense, creatures that grapple you or hits you with a melee weapon attack while within 5ft. of you takes 1d6 piercing damage.

Rage
In battle, you fight with primal ferocity. On your turn, you can enter a rage as a bonus action.

While raging, you gain the following benefits if you aren't wearing heavy armor:

You have advantage on Strength checks and Strength saving throws.
When you make a melee weapon attack using Strength, you gain a +2 bonus to the damage roll. This bonus increases as you level.
You have resistance to bludgeoning, piercing, and slashing damage.
If you are able to cast spells, you can't cast them or concentrate on them while raging.

Your rage lasts for 1 minute. It ends early if you are knocked unconscious or if your turn ends and you haven't attacked a hostile creature since your last turn or taken damage since then. You can also end your rage on your turn as a bonus action.

Once you have raged the maximum number of times for your barbarian level, you must finish a long rest before you can rage again. You may rage 2 times at 1st level, 3 at 3rd, 4 at 6th, 5 at 12th, and 6 at 17th.

Unarmored Defense
While you are not wearing any armor, your Armor Class equals 10 + your Dexterity modifier + your Constitution modifier. You can use a shield and still gain this benefit.

Expertise
At 1st level, choose two of your skill proficiencies, or one of your skill proficiencies and your proficiency with thieves' tools. Your proficiency bonus is doubled for any ability check you make that uses either of the chosen proficiencies.

At 6th level, you can choose two more of your proficiencies (in skills or with thieves' tools) to gain this benefit.

Sneak Attack
Beginning at 1st level, you know how to strike subtly and exploit a foe's distraction. Once per turn, you can deal an extra 1d6 damage to one creature you hit with an attack if you have advantage on the attack roll. The attack must use a finesse or a ranged weapon.

You don't need advantage on the attack roll if another enemy of the target is within 5 feet of it, that enemy isn't incapacitated, and you don't have disadvantage on the attack roll.

The amount of the extra damage increases as you gain levels in this class, as shown in the Sneak Attack column of the Rogue table.

Thieves' Cant
During your rogue training you learned thieves' cant, a secret mix of dialect, jargon, and code that allows you to hide messages in seemingly normal conversation. Only another creature that knows thieves' cant understands such messages. It takes four times longer to convey such a message than it does to speak the same idea plainly.

In addition, you understand a set of secret signs and symbols used to convey short, simple messages, such as whether an area is dangerous or the territory of a thieves' guild, whether loot is nearby, or whether the people in an area are easy marks or will provide a safe house for thieves on the run.

Danger Sense
PHB p46
At 2nd level, you gain an uncanny sense of when things nearby aren't as they should be, giving you an edge when you dodge away from danger. You have advantage on Dexterity saving throws against effects that you can see, such as traps and spells. To gain this benefit, you can't be blinded, deafened, or incapacitated.

Reckless Attack
PHB p46
Starting at 2nd level, you can throw aside all concern for defense to attack with fierce desperation. When you make your first attack on your turn, you can decide to attack recklessly. Doing so gives you advantage on melee weapon attack rolls using Strength during this turn, but attack rolls against you have advantage until your next turn.