As stated in the post on Chinese Commanderies and Confederated Cingdoms in Corea, the Gaya Confederation evolved out of the twelve states in the Byeohan Confederation, which was one of the Samhan states. The traditional founding date for Gaya is 42 AD, which stems from the Samguk Yusa's legend about the founding of the confederacy. However, archeological evidence suggests that the transition from Byeohan to Gaya took place sometime during the end of the 2nd century. There is considerably less information available on Gaya than on the Three Kingdoms because the Samguk Sagi does not include a history of Gaya. Nonetheless, here's a summary of what I was able to uncover.
Overview of Gaya
Six or Seven or More
The Gaya Confederation was situated in the Nakdong river ( 낙동강 ) basin, which is in the southeast portion of the Korean peninsula near the location of modern-day Busan. The confederation is usually considered to have contained the six Gaya kingdoms, which are: Ara Gaya ( 아라가야 ), Goryeong Gaya ( 고령가야 ), Dae Gaya ( 대가야 ), Seongsan Gaya ( 성산가야 ), So Gaya ( 소가야 ) and Geumgwan Gaya ( 금관가야 ). However, a seventh kingdom, Bihwa Gaya ( 비화가야 ), is also mentioned in the Samguk Yusa and archeological evidence suggests that were probably more than ten states within the confederation.
The Samguk Yusa tells a story in which the nine chieftains who ruled Gaya gathered together to select a king in the year 42 AD. A voice from heaven told them that they could find a king if they dug into the ground at Gujibong peak. The chieftains found six eggs at the peak. The boys that were born from these eggs were apparently already destined to become kings and they reached maturity within twelve days of their birth. One of the boys was named Suro ( 수로 ) and he went onto to become the king of Geumgwan Gaya. The other five boys each started their own state and these six states became known as the Gaya Confederation.
The states that formed the early Gaya Confederation, also known as the Byeohan Confederation, date to the first century AD, but they probably did not form an actual confederation until the end of the second century or beginning of the third century. Byeohan consisted of twelve states and the most powerful of these states was called Garak-guk (later to be known as Geumgwan Gaya), which was also known as Gaya-guk or Guya-guk, and was located at modern-day Gimhae. Garak-guk's power has been attributed to its advantageous location and its advanced iron-working technology. Garak-guk was located on the southern coast of Korea and therefore was in a great location for trade with both Japan and China. This location also had access to iron which, when combined with Garak-guk's advanced knowledge of iron-working, contributed to Garak-guk's powerful status in the region.
Downfall of Early Gaya
Gaya became allied with Baekje and Wa (Japan) and this alliance caused Silla to request help from its northern neighbor, Goguryeo. Gwanggaeto the Great of Goguryeo, responded with 50,000 troops in 400 AD and this led to the downfall of early Gaya. Since Gaya had never become a fully unified state like the Three Kingdoms, it lacked a strong military and therefore easily succumbed to Goguryeo's military might. Not all of the states were conquered, but the eastern portion of the confederation became part of Silla and the most powerful states were completely destroyed. The inhabitants of these conquered states either moved inland or headed across the Korea Strait to Japan and took their iron-making technology with them.
Reemergence of Gaya
The Gaya Confederation arose once again in the second half of the fifth century, this time with Dae Gaya (previously named Banpa-guk) as the most powerful state. Dae Gaya even assissted its previous enemy, Silla, against an invasion attempt by Goguryeo at the end of the fifth century. Dae Gaya then went so far as to create marriage ties with Silla in 522, but this relationship quickly disintegrated.
Downfall of Gaya
Parts of Gaya started to come under Baekje rule in the 530s and the confederation eventually split into two parts in the 540s, with a Dae Gaya led faction in the south and Ara Gaya leading the northern parts of the confederation. The states attempted to reunite, but were conquered by Silla prior to any unification, with the last states falling under Silla control in 562.
The Fourth Kingdom?
So does Gaya deserve to be mentioned alongside Goguryeo, Baekje and Silla as one of the ancient kingdoms of Korea? Well, it never attained the size or solidified political structure of these three kingdoms. However, for a few centuries it flourished alongside its neighbors and even attained superior metal technology. It also was a mecca for Korean trade with both China and Japan. It even played a role in many of the alliances formed between the kingdoms during the near-constant hostility that took place in those years. A credible case could be made on Gaya's behalf and at the very least it should not be considered the "lost kingdom" as it has come to be known because it certainly played an important role during this time period in Korean history.
A Closer Look at the States
This state was founded by King Suro in 42 BC and was originally known as Garak-guk. It was the most influential state during the early years of the Gaya Confederation. Garak-guk's location at modern-day Gimhae provided it with easy access to parts of Korea along the Nakdong river and to Wa in Japan. Archeological evidence suggests that Garak-guk was engaged in a war against Silla at the end of the third century. The state then realigned itself and became allies with Silla during the first half of the fourth century and later proceeded to again become enemies with their neighbor by the end of the fourth century. The demise of Garak-guk occurred in the year 400 when Gwanggaeto the Great of Goguryeo sent 50,000 troops against the small state. The state was revived in the latter half of the fifth century when Dae Gaya developed into a powerful force in the region. However, Dae Gaya's alliance with Silla quickly fell apart and Silla sent an army to conquer Geumgwan Gaya. Rather than resist, King Guhae of Geumgwan Gaya accepted the inevitable and surrendered to Silla in 532. Silla granted King Guhae and his family the rank of "true bone", which was the second highest rank in the Silla Bone Rank System. Another interesting fact is that Kim Yushin, who was the general during Silla's defeats of Baekje and Goguryeo, was the great-grandson of King Guhae.
Dae Gaya was originally known as Banpa-guk during the early years of the Gaya Confederation, but later changed its name to "Great Gaya". Dae Gaya was founded by King Ijinashi in 42 AD and developed into a culturally rich and technologically advanced society. Its cultural influence is still seen today in the Gayageum, which is a musical instrument that was created in Dae Gaya during the sixth century. This was the most powerful Gaya state in the later part of the Gaya Confederation and it participated in alliances with both Baekje and Silla. The first alliance was formed with both of these kingdoms in 481 AD when the states combined in a battle against Goguryeo. Dae Gaya then allied with Baekje in 554 in its battle against Silla, but this alliance was defeated and it ultimately provided a reason for Silla to invade and conquer Dae Gaya in 562.
Initially named Anla-guk, Ara Gaya was one of the northern states in the Gaya Confederation. In contrast to the other powerful states of Gaya, Ara Gaya initially decided upon a diplomatic foreign policy with the neighboring Baekje and Silla kingdoms and attempted to maintain peaceful relations with both states. However, the split of the Gaya Confederation and the increasing influence of Baekje led Ara Gaya to seek an alliance with Goguryeo. Unfortunately, Goguryeo failed in its 548 invasion attempt of Baekje and Ara Gaya was not able to recover any of the land it had lost to Baekje. Silla's defeat of Baekje in 554 eventually led to Silla's invasion of Gaya and Ara Gaya surrendered to Silla in 559.
Goryeong Gaya was situated in the northern portion of the Gaya Confederation and also sought to maintain peace with the neighboring kingdoms. Goryeong Gaya developed marital ties with Silla in 522 and did not participate in Baekje's battle against Silla. Unfortunately, this does not seem to have ultimately done any good, as Goryeong Gaya was conquered by Silla in 562.
I couldn't find much information on this state, but it apparently had close ties with Silla. For this reason, it did not fight against Silla, but it still seems to have met the same demise as the other Gaya states.
Again, virtually no information (at least in English) on this state, but I was able to gather that this state did participate with Baekje in its struggles against Silla and therefore was probably conquered by Silla around the same time as the other states. The following I got from a Google translation of a Korean page on So Gaya and it was a pretty poor translation, so I'm not sure if this is completely correct, but it was the most information I could find. I believe it stated that So Gaya was founded as early as 9 AD and was conquered by Silla in 562 AD. There was other information on various battles, but it was so poorly worded that I couldn't really understand it.
A New History of Korea by Ki-baik Lee
The Distribution Chart of Gaya by Taesik Kim
A History of the Gaya Kingdoms: A Brief Survery by Taesik Kim
Geumgwan Gaya's History by Taesik Kim
Gaya Kingdom's Rightful Place in Korean History by Taesik Kim
Discovering the History of Gaya through its Legends by Kim Doo-jin
Gaya History and Culture
And of course our old pal, Wikipedia