Object used and are in AoT(Signal Flare)

Signal Flare:

The Signal Flare is a common tools used in the Military by the Garrison and the Survey Corps. The signal flare has a variety of uses depending on the mission.

Uses:

While the Signal Flare has many uses, its main purpose is long distance communication. The Garrison uses it as a way to inform the higher-ranking officers how their mission is going while the Survey Corps uses it as a way to communicate (often in the presence of Titans) to the rest of the legion.

Ammo:

The ammo used depends on the mission at hand. The ammo the Garrison uses is the following:

• Green - Mission started.
• Red - Mission failed.
• Yellow - Mission successful.

The ammo the Survey Corps uses for the 57th expedition beyond the Walls is the following:

• Red - Titan spotted.
• Black - Deviant Type Titan spotted.
• Purple - An emergency of some kind.
• Blue - An order to retreat.
• Green - Change direction of the formation: Fired by the commander in one direction to indicate a change in the direction, and then repeated by the relay soldiers.
• Yellow - This lets everyone know that the mission has been terminated, be it successfully or failed.
• While leading the Female Titan through the Forest of Giant Trees, Levi used a special shell that emitted a high-pitched noise.

Objects used and are in AoT(Cannons)

Cannons:

Cannons were the primary weapon used to engage Titans before the development of the 3D maneuver gear.

Despite the ability of a cannon to blow a Titan's head off in one shot, half of all Titans will merely regenerate their heads; the only certain way to kill a Titan is to destroy the nape of its neck. Cannons are still used in static defense poistions, most notably on the Walls and near gates during Wall breaches. As such, they are used most often by the Stationary Guard.

The cannons contain two different rounds: pomegrenades and grapeshots. Pomegrenades are high explosive rounds used to attempt to kill a Titan by destroying the nape of the neck in the blast. Grapeshots are the more traditional cannon round and are mostly used to slow down Titan advances with their wide dispersion shots.

Before firing, the cannon must be solidly fixed to prevent the recoil from blowing it off the tracks. Wall-mounted cannons also possess the ability to fire directly downward, which can allow them to release punishing volleys of fire at Titans with no threat of reprisals.Later developments led to railroads encircling the entire Wall, allowing cannons to bunch together and focus fire.Prior to the breach of Wall Maria, Wall-mounted cannons had limited mobility and could only fire from one point inside or outside the Wall.

During the breach of Trost District, the Colossal Titan disabled the railroads on top of the Wall to prevent reserve cannons from being brought in.

Objects used and are in AoT(Firearms)

Firearms

Because firearms are unsuitable for dispatching Titans, they have not progressed very far technologically and are almost always overshadowed by the Three Dimensional Maneuver Gear. However, they are still regularly used by the Military Police and other human-to-human security relations. The Survey Corps also uses flareguns to communicate over long distances.

The type of firearm used is based on the flintlock mechanism, where a piece of flint ignites the powder and fires the gun, which must be reloaded after every shot. Currently, rifles (or muskets) and pistols are the only firearms seen in the story.

Although the firearms within the walls are low-tech, they do have some modern applications. During the battle of Trost, one of the most notable features of the firearm is the lack of smoke it produces. Indicating that it uses modern gunpowder, which creates a large flash, compared to black-gunpowder which produces a massive cloud of smoke when fired. 

Firearms are unable to kill Titans because they lack the power to punch through the nape of the neck (a Titan's weakness). Also, given a Titan's fast regeneration rate and the long amount of time it takes to reload a flintlock weapon (15-30 seconds), they are practically useless in dealing enough lasting damage to severely harm a Titan. However, they can shoot out a Titan's eyes and blind it until it regenerates them.

Objects used and are in AoT(SnK)(Three Dimensional Maneuver Gear)

Three Dimensionsal Maneuver Gear(3DMG):

The Three Dimensional Maneuver Gear (立体機動装置 Rittai kidō sōchi^?), also called Vertical Maneuvering Equipment, is a set of gear developed by humans that allows great mobility when facing the Titans in combat. The gear allows the user to fight in a 3D space as opposed to a 2D one. The gear itself takes the form of a body harness that encompasses much of the body below the neck. Though using it will allow a skilled user great mobility, it carries a large risk of overtaxing the user's muscles, thus special physical conditioning is required to use this gear. Some tools involved in the apparatus include:

• Handgrips 
• Piston-shot grapple-hooks
• Gas powered mechanism
• Iron Wire Propeller with Plug in Blades

Usage:

The simplest move possible with the 3DMG is simply aiming and firing the grapple hooks at an object and then activating the gas mechanism to reel oneself toward said object. They can then disconnect the hook and continue moving forward.

Usually however, soldiers must be able to move around in order to navigate in general. Therefore, they tend to use their momentum in order to swing around targets.

More advanced techniques include changing directions while still being reeled in as demonstrated by Jean Kirstein.

Levi often uses a very advanced technique. After hooking the wire onto the Titan's neck, he releases the hook, and does 2~3 spins. Finally, he strikes down on the Titan, killing it.

Origin:

The circumstances regarding the creation of the 3DMG are detailed in the prequel novel Before The Fall. 3DMG was invented between 775 (year of the Titan attack and BTF's prologue) and 788 (13 years later) by Angel Aaltonen, a first-class weapons craftsman who worked closely with the Survey Corps.

Mechanics:

The Body of the Device - Steel wire is stored inside the body. There are two axles, which revolve independently. 

Operating Device - The functioning part of the operating device is a black box, which the technical department manages and improves in secrecy.

Body of the Compressed Gas Cylinder - Gas is compressed into the cylinder and injected.

Fan Section - Gas is blown directly into the fan to make it rotate. The pressure of the gas is regulated to manipulate the output.

Training:

Three-dimensional maneuver device training is a rigorous process that allows humans, which are limited to two-dimensional movements, to adapt to movement in the third dimension. 

Great physical strength, particularly in the legs, coupled with spatial recognition abilites, as well as the mental strength to not waver in the midst of a panic, are crucial qualities.

One of the first things done after enlisting in training is the 3D Maneuver Gear aptitude evaluation. Those unable to remain upright are dismissed.

"Those incapable [of staying upright] aren't suited to even be used as decoys!"

Three years of training is needed before officially becoming a soldier. Many run away or are driven out before graduating. The training is so intense that some people actually die during the process.

The organizations in AoT(SnK)(Military Police Brigade)

Military Police Brigade:

The Military Police Brigade (憲兵団 Kenpeidan^?) is the most prestigious due to their work allowing them to live safely within the Inner Wall, abundant resources, and higher authority over other military sectors. However, in reality it is the most corrupted military sector due to a lack of oversight compared to the other sectors of the military. Due to their misuse and abuse of authority, the Military Police Brigade is also at odds with Garrison and especially with the Survey Corps. Only the top ten alumni from trainee squads can apply for the Military Police Brigade. However, according to the conversation between Hitch and Boris, there are other (illicit) ways to get in the sector such as fraternization, favouritism, etc.

Duty:

The Military Police Brigade is the primary police force within human territory. Not only do they maintain order, they serve as the king's guard. Since they do not normally come in contact with Titans, they must have special permission to use 3D gear and usually carry firearms such as rifles instead. They are also in charge of tax collection and land distribution as seen in Ch. 15 when a couple of policemen monitored farm production. They usually abuse these duties to exploit resources and food from civilians.

In Episode 25, Wall, their assigned duty was changed due to the mass destruction caused by Eren and Annie. From guarding the Recon Corps, they were ordered by Nile Dok to evacuate all civilians and bringing Commander Erwin on the trial to set punishment for his plan to capture the Female Titan.

However these duties were abused by the Military Police Brigade officials, as it is in their nature.

Structure:

The Military Police Brigade is an organization with 2,000 members, with direct command over 3,000 additional personnel from the Garrison. This brings their total potential manpower to 5,000 soldiers. Their forces are divided between the major Districts, with 200 officers assigned per District.

The Central Branch operates completely separate from the main group, with their own command structure and duties. Little is known about them, with even Nile Dok admitting to knowing little about them. They are involved in numerous conspiracies, and stated to be completely above the law. They are rarely seen outside the Capitol.

Qualities:

The Military Police Brigade is supposed to be an elite unit made of the most skilled soldiers due to its rigorous standards. The reality though, is a lazy, corrupt system that benefits from the powers granted to it. Though they are top ten graduates from the trainee squads; they are inexperienced since they only stay in the safety of Wall Sina and never engaged in battle with the Titans before.

The senior officers spend all their time gambling and drinking while leaving recruits to do all the work. They also pilfer taxes and misappropriate land as a recruit, Marlowe Freudenberg, mentions in Ch. 31. This corruption is well-known with many people (even to Wall Sina citizens) criticizing their lack of care for anyone other than themselves. Refugees and forced laborers (called producers) hold simmering hostility against them.

However, many trainees still dream of joining the Military Police Brigade because it will allow them to live within Wall Sina and safety. Also, being so close to the center of human territory, most policemen have relatively little experience fighting Titans as compared to the Survey Corps or the Stationary Guard. This, together with corruption, loose discipline, contempt from public, abuse of power makes this military branch the most incompetent out of the three.

However, by Ch.45, it's revealed that the King becomes tougher on the Military Police for their lack of diligence in dealing with their corruption, lack of discipline, pilfering of taxes and mismanagement of lands. He orders them to leave the safety of Wall Sina and assist both the Survey Corps and the Stationary Guards to look for the two other traitors in collaboration with Annie. By the end all three factions have banded together to help rescue Eren and Ymir from Reiner and Bertolt.

In chapter 47 of the manga, all their shortcomings and negligence of trainings are brought to light; most personnel from Military police are all too easily slaughtered by Titans even before the rescue operation began in earnest. In episode 24 of the anime, when a Female Titan suddenly appeared in Wall Sina and went on a rampage that caused Wall Sina's terrified citizens to flee chaotically in all directions most (if not all) of military police personnel, afraid and completely at a loss of what to do, just stood transfixed and did nothing to alleviate the problem.

The Central Branch is introduced in the aftermath of the traitors' being exposed, torturing and murdering Pastor Nick. Their organization is shrouded in mystery, and they actively seek out both Historia Reiss and Eren Yeager for unknown purposes. They have been shown to be far more skilled and disciplined than the rest of the military police, though their main skills are in fighting other humans than Titans. With the Titan Shifters uncovered and driven out, this mysterious group appears to be the new antagonists of the series.

The organizations in AoT(SnK)(Garrison)

Garrison:

The Garrison (駐屯兵団 Chūton Heidan^?), also known as the Stationary Guard, is the largest of the Military divisions which protects and maintains order near the Walls. Given the fatality rate of the Survey Corps and the limited entry of the Military Police Brigade, most soldiers join the Garrison. As they often have close contact with both Titans and human civilians, they are proficient over a wide variety of tasks such as Titan combat (defensive battles), cannonading, security detail, crowd control, and rifle usage.

Duty:

The Garrison takes care of all defences for the Wall whether it be patrols, repairs, or improvements. As such, they spend most of their time preparing for attacks against the Wall. The Garrison mans the cannons on the Wall that are often used for long-range Titan defence. They must also deal with civilian evacuation and have emergency plans for dealing with scenarios for when the Wall is breached.

Structure:

The Garrison is the largest of the three branches, with a total of 30,000 soldiers. Members of the Trainee Corps are considered in this total, until their graduation and enlist in a chosen branch. Their total number of combat-ready personnel is a mere 3rd of this total, at 10,000 soldiers.

Their structure consists of Regiments, Brigades, and Divisions. A regiment is the smallest unit, consisting of 1000 soldiers. A Brigade consists of anywhere between 2,000 and 3,000 soldiers, or 2-3 regiments. And finally, the largest units are Divisions, which consist of 2 Brigades.

Qualities:

Being the main fighting force of the 3DMG soldiers, the men and women of the Garrison come from all backgrounds and views. Most are simply afraid of dying or unwilling to give their lives for what they believe to be foolish causes, although many are fiercely devoted to the protection of mankind, having joined the Garrison simply to protect loved ones from the threat of Titans. The great deal of diversity also gives great talent to the Garrison: imaginative and magnetic men like Dot Pixis are present and successfully motivate their subordinates to do their duty.

Before the fall of Wall Maria due to a horrific Titan raid, the quality of the troops were lax, lazy, undisciplined, and unreliable; only slightly better than the Military Police Brigade. All that changed after Wall Maria fell. Since then, the Garrison has become innovative, tactical/strategic, diligent, disciplined, competent and purposeful. This branch is currently the second most reliable military branch along with the Survey Corps.

Tactics:

The only case of members of the Garrison coming into contact with Titans will come from a direct confrontation due to a breach in the Wall. As such, their tactics are intertwined with civilian evacuation and Titan defenses.

Special Colossal Titan Strategy

The soldiers will be arrayed to fight by skill level with soldiers increasing in skill level the closer to the evacuation point. The Front Gaurd is made of regular Stationary troops. The Middle Guard incorporates the more advanced trainers. Finally, the Rear Guard protects the base of the Wall with the elite Garrison squads.In the case of a breach, the Garrison must mobilize its men to confront the Titans coming in. If there is no way to block the breach, then direct battle must be conducted to give enough time for all civilians in the town to escape. Upon the successful evacuation of all civilians, the gate will be closed and the district will be quarantined. It is only then that all the soldiers may escape to the safety of the Wall.

While this is going on, all attempts to stop outside Titans from entering the district short of fighting them with 3DMG will be used. This includes methods such as cannon bombardment and harpoon nets to stop Titans in their tracks by impaling them and preventing other Titans from coming through.

Outer Wall Breach Emergency Plan

Because the Wall is so large, the Garrison simply does not have the manpower to patrol every section. That is why districts are outcroppings of the Wall - to make Titan monitoring easier as they are naturally attracted to areas of concentrated humans. However, in Ch. 34 when the Wall is breached outside a town, this plan must be used.

The main priority of the Garrison is to safely transport everyone to the next secure Wall. Failure to do so will isolate and eventually lead to the settlement being overrun, and not only the settlement, but perhaps even the entire area within the wall. Meanwhile, the breach must be located in order to plan the next move.

The organizations in AoT(SnK)(Military Police)

Military Police:

Humanity's defense against Titans is a full-time, professional army trained to deal with Titans. The Military is divided into three divisions: the Survey Corps, which explores outside human territory to hostile areas in a bid for expansion, lately receiving a new mission from the Capital to research the Titans and where they originate from; the Garrison, which patrols and maintains the Walls keeping Titans out and acting as the first to engage the Titans if the gate is destroyed; and the Military Police, the top-ranking soldiers who serve as the personal guards for the king and maintain order within the Walls.

Uniform and Equipment:

All members of the Military, excluding the Training Corps Instructors, wear similar uniforms consisting of a short, light brown jacket with the badge of the squad on both shoulders, on the front left pocket and on the centre of the back, a light-coloured shirt, a dark brown sash around the waist covering the hips, white pants, and dark brown knee-high leather boots. The Training Corps Instructor Uniforms differs slightly from the other branches, including an olive-green trench coat replacing the jacket of the other factions. The Survey Corps members often wear a heavy, green, hip-length hooded cloak with their symbol on the back, usually when conducting missions outside of human territory. Trainees have been observed to wear the cloaks, albeit without any symbols, when conducting marches in the rain.

The main equipment of the Military is the Three Dimensional Maneuver Gear, which is also their main weapon used in conjunction with two snap-off blades attached to the handgrips. However, the Military Police often use rifles since they mostly deal with people and rarely with Titans.