The Gokyo are the 40 throws of Judo. They are split into 8 sets of 5, hence "go" kyo.
There are about 100 throws in Jujutsu, some of which are variations on a basic theme.
40 of these throws made the Judo gokyo, the safe format that can be used competitively in randori and shiai. You learn the gokyo in Judo as your syllabus on the way to your black belt.
However Judoka pick only 2 or 3 throws to focus on for their use in randori, with 2 or 3 as backup. Nobody tries to perfect all 40 throws for daily use. In fact, most competitors don't start to really examine the gokyo until they retire from competition and start working on getting their higher dan grades.
In STMA we have picked the most applicable throws whcih work in randori and have combat application.
Judoka who train with us need to keep in mind that what we practice is Jujutsu not Judo and we are ultimately interested in combat throws not competition moves.
We also practice throws without the gi jacket, using the "wrestling concept" of collar and elbow tie up.
Finally, in a Judo match you will be against another skilled grappler fighting for throws. Your opponent on the street will not be a skilled grappler. He will also not be restricted to grappling and will be trying to strike you and maybe have a weapon. This is fine with us as we practice Atemi strikes "Blow before throw", such as HKE.
GOKYO
The standard syllabus of Judo throws originated at the Kodokan in 1895.
The Gokyo of 40 throws in 5 groups of 8 was established in 1920
Dai ikkyo - 1st group
1.Deashi harai
2.Hiza guruma
3.Sasae tsurikomi ashi
4.Uki goshi
5.Osoto gari
6.O goshi
7.Ouchi gari
8.Seoi nage
Dai nikyo - 2nd group
1.Kosoto gari
2.Kouchi gari
3.Koshi guruma
4.Tsurikomi goshi
5.Okuriashi harai
6.Tai otoshi
7.Harai goshi
8.Uchi mata
Dai sankyo - 3rd group
1.Kosoto gake
2.Tsuri goshi
3.Yoko otoshi
4.Ashi guruma
5.Hane goshi
6.Harai tsurikomi ashi
7.Tomoe nage
8.Kata guruma
Dai yonkyo - 4th group
1.Sumi gaeshi
2.Tani otoshi
3.Hane makikomi
4.Sukui nage
5.Utsuri goshi
6.O guruma
7.Soto makikomi
8.Uki otoshi
Dai gokyo - 5th group
1.Osoto guruma
2.Uki waza
3.Yoko wakare
4.Yoko guruma
5.Ushiro goshi
6.Ura nage
7.Sumi otoshi
8.Yoko gake
Habukareta waza - preserved techniques from 1895 which were readded to the Kodokan syllabus in 1982
1.Obi otoshi
2.Seoi otoshi
3.Yama arashi
4.Osoto otoshi
5.Daki wakare
6.Hikikomi gaeshi
7.Tawara gaeshi
8.Uchi makikomi
Shinmeisho no waza - 17 newly accepted techniques in 1987, two in 1997 and one in 2017
1.Morote gari
2.Kuchiki taoshi
3.Kibisu gaeshi
4.Uchi mata sukashi
5.Tsubame gaeshi
6.Kouchi gaeshi
7.Ouchi gaeshi
8.Osoto gaeshi
9.Harai goshi gaeshi
10.Uchi mata gaeshi
11.Hane goshi gaeshi
12.Kani basami
13.Osoto makikomi
14.Kawazu gake
15.Harai makikomi
16.Uchi mata makikomi
17.Sode tsurikomi goshi
18.Ippon seoinage
19.Obi tori gaeshi
20.Kouchi makikomi
Daki age - now excluded
The KODOKAN list makes a total of 69 throws, if Daki Age is included
There are a further 31 throws that were in the Original Kodokan list of 100 Nage, that are technically still Judo throws, though not included or taught at the Kodokan