The aikido we teach contains, just as Mr. Tomiki envisioned, a series of kata as well as the practice of randori (although, unlike common Tomiki-ryu schools, we pursue a non-competitive form of randori). As with judo, randori serves as a method of applying principles learned by long repetition of kata. Within the kata are a wide range of technical applications which include:
Nage Waza Throwing Techniques
Katame Waza Locking Techniques
Atemi Waza Striking Techniques
Kansetsu Waza Joint Techniques
Suwari Waza Kneeling Techniques
Tachi Waza Standing Techniques
Ukemi Waza Falling Techniques
Tatno Waza Defending Against a Knife
Tachi Dori Defending Against a Sword
Jo no Bu / Jo Dori Defending Against a Jo
Jo no Bu / Jo no Tsukai Kata Using a Jo
Tachi no Tachi Sword Against Sword
Those techniques, in turn, are represented in the following aikido kata:

Tegatana no Kata The Walking kata
Hanasu no Kata The 8 Releases
Ju Nana Hon Kata The 17 Main Forms
O Waza Ju Pon The Big 10

Below are listed the advanced katas which are studied from Shodan onward: 

Koryu Dai San The Third Advanced Kata
Koryu Dai Yon The Fourth Advanced Kata
Koryu Dai Go The Fifth Advanced Kata
Koryu Dai Roku The Sixth Advanced Kata

Tegatana no Kata
1) Shomen Ashi forward step feet only 
2) Waki Ashi side to side step feet only 
3) Tenkan Ashi step  feet only 
4) Shomen Te Gatane straight hand blade same hand/ foot
5) Uchi Mawashi inside sweep hand blade same hand/ foot
6) Soto Mawashi outside sweep hand blade same hand/ foot
7) Uchi Soto Gaeshi forward block & side push same hand/ foot
8) Uchi Mawashi Gaeshi inside sweep & turn same hand/ foot
9) Soto Mawashi Gaeshi outside sweep & turn opposite hand/ foot 
10) Ude Goshi Gaeshi arm & hip turn opposite hand/ foot 
11) O Mawashi major circle  opposite hand/ foot 
12) Yoko O Mawashi side major circle both hands/ feet 

Hanasu no Kata
1) Hon Soto Hanasu normal outside release palm down 
2) Hon Soto Te Osu normal outside hand push palm up 
3) Gyaku Soto Hanasu reverse outside release palm up 
4)Gyaku Soto Te Osu revearse outside hand push palm down 
5) Hon Uchi Hanasu normal inside release palm down 
6) Hon Uchi Ude Hineri normal inside arm twist palm up 
7) Gyaku Uchi Hanasu revearse inside release palm up 
8) Gyaku Uchi Ude Hineri revearse inside arm twist palm down 

Ju Nana Hon Kata
Ateme Waza Striking Techniques
1) Shomen Ate straight frontal head strike
2) Aigamae Ate regular facing posture strike
3) Gyaku Gamae Ate revearse posture strike
4) Gedan Ate low strike 
5) Ushiro Ate behind (from the rear) strike
Hiji Waza Elbow Techniques
6) Oshi Taoshi knock or push down
7) Ude Gaeshi arm turn 
8) Hiki Taoshi pull and push down
9) Ude Hineri arm twist 
10) Waki Gatame side of chest arm lock

Tekubi Waza Wrist Techniques
11) Kote Hineri wrist twist 
12) Kote Gaeshi wrist turn 
13) Tenkai Kote Hineri circular wrist twist
14) Shiho Nage four corner (all directions) throw

Uki Waza Floating Techniques
15) Mae Otoshi forward drop 
16)Sumi Otoshi
rear corner drop
17) Hiki Otoshi pull and drop wheel

O Waza Ju Pon
1) Kubi Guruma neck wheel
2) Kata Otoshi shoulder drop
3) Ude Guruma arm wheel
4) Hiji Guruma elbow wheel
5) Aiki Nage fitting in throw 
6) Shiho Nage four corner (all directions) throw
7) Ushiro Ate  behind (from the rear) stirke
8) Kote Gaeshi wrist turn
9) Ushiro Kubi Gatame hold from behind (the rear)
10) Shizumi Otoshi  sinking body drop