The pace of the Hiten Mitsurugi ( Flying Heaven's Honorable Sword Flow) sword skill is extremely fast. The moves can be divided into four main parts. There are different names of moves in each part.

The first part is called Ran-Geki-Jutsu, which means to wield the sword to attack sequentially at once. Moves that belong to Ran-Geki-Jutsu are:

Ryu-Kan-Sen (Dragon Wind Up Flash) :
A technique used once one has gotten beside an opponent, it involves a very powerful swing with the twist of your whole body, inflicting a direct blow under the skull.
Do-Ryu-Sen (Ground Dragon Flash):
A technique where it strikes the ground and with the force of the strike, the ground will explode toward the opponent.
Ryu-Sou-Sen (Dragon Double Flash):
This involves multiple slashes to its opponent, without giving the opponent the chance for a counter attack. It is effective in dealing with those who will not get knocked out with one move.

The second part is called Totsu-Shin-Jutsu, it means to attack immediately and just wield the sword once. Skills of this part are:

Ryu-Tsui-Sen (Dragon Mallot Flash) :
This move is like a Dragon diving into its opponent from the sky and hammering by using its weight.
Ryu-Kan-Sen Tsumuji (Dragon Wind Up Flash Hair-spin):
Ryu-Kan-Sen-Tsumuji is another variety of Ryu-Kan-Sen. It begins by dashing into an opponent without gravity and at a tremendous speed. After getting into position beside your opponent, a Ryu-Kan-Sen will be performed. The damage is more powerful than Ryu-Kan-Sen, due to its speed. However, landing poses a problem due to its speed.
Tsumuji=Gyrate
Ryu-Sho-Sen (Dragon Rising Flash) :
This move is like a dragon that lifts up into the air with the blade of the sword attacking its opponent's vital points with the force of its jump.

The third part is called Battou-Jutsu (Sword Skill), Battou - an instant sword draw. Jutsu - technique. In a stance form and waiting for an opponent with the correct timing, a powerful swing with the twist of waist. It is the skill to attack by drawing the sword. The names of the skills in this part are:

Hi-Ryu-Sen (Flying Dragon Flash):
This move may be accomplished using the left hand only (as in the fight with Raijyuuta). As you twist your body around, the sword is sprung from the sheath with the left hand coupled with the centrifugal force, so the key here is to aim the hilt of the sword at your opponent's weak point, like between the eyes.
Sou-Ryu-Sen (Paired Dragon Flash):
Sou-Ryu-Sen is one of the variaties of Battou-Jutsu. Sou-Ryu-Sen contains double attack with the sword and the sheath. It is best used when the sword is blocked then without moment of waste, the second Battou-Jutsu using the sheath will strike the opponent. If I'm not wrong, Kenshin invented this move while fighting with Kurogasa.
Sou-Ryu-Sen Igazuchi
Igazuchi=Thunder

The last part is the most important and powerful skill in which the master can be killed while passing on this skill to the student:

Ouki Ama-Kakeru-Ryu-No-Hirameki (Heaven's Soaring Dragon Flash):
The succession technique. The secret of the Ama-Kakeru-Ryu-No-Hirameki is revealed by Soujirou after his last fight with Kenshin. Normally, when using the Battou-Jutsu, the right leg is placed in front of the left leg so to avoid cutting your own leg (since the sword is at the left side). However, at the very last moment of attack, Kenshin placed his LEFT leg in front of his RIGHT leg before drawing his sword, thus bringing the speed and might of the sword to its very maximum. At that very moment, he must calculate the MOMENT of attack and how to twist his body properly in order not to cut himself. To do this, he must possess a strong desire to live.
Ouki=profoundness

Before passing on the above skill to Kenshin, Hiko Seijuurou showed another skill to Kenshin:

Ku-Zu-Ryu-Sen (9 Headed Dragon Flash):
This is a move that was taught before the succession technique. It is to wield the sword nine times from nine different directions at once and strike all nine vital points all instantly. Because of that, it is impossible to dodge or to defend this certain move. According to Hiko, since this move is completely impossible to be avoided or blocked, the only way to break it is by making one's move before one's opponent uses the 9 Headed Dragon Flash, i.e. by using a Battou-Jutsu which surpasses the "God-like Speed".

In each generation heritage of Hiten Mitsurugi Ryuu, the master is always killed by the student (the next inheritor) after passing on the most powerful skill.

In manga volume 17, which is about the end of fighting between Shishio & Kenshin, Kenshin uses 5 new moves (5 new names).

I don't know where these 2 moves fit in, please help!
Ryu-Tsui-Sho-Sen (Dragon Mallot Rising Flash):
This is a combination of Ryu-Tsui-Sen and Ryu-Shou-Sen. It begins by attacking the opponent on it's way down from the air with Ryu-Tsu-Sen. When it lands, Ryu-Sho-Sen will be performed to give the opponent twice the damage. It's an up and down attack.
Ryu-Kan-Sen-Arashi (Dragon Wind Up Flash Storm):
Ryu-Kan-Sen-Arashi is similar to Tsumuji although Arashi is more like an aggressive style of Tsumuji and probably more damaging than Tsumuji.