Pradyumna is the name of a character in the Srimad Bhagavatam. He was the son of Lord Krishna and Rukmini. Pradyumna is considered as one of the four vyuha avatar of Vishnu. When he was a baby he was abducted by the demon Sambara. He was then cast into the sea and swallowed by a fish, but that fish was caught and carried to the house of Sambara. The fish was opened and the child was found inside. He was given to a woman in Sambara's house to raise. Narada informed her about the true identity of the child. When Pradyumna grew up, he battled the demon Sambara, defeated him. Pradyumna was later killed in a brawl in his father's court at Dwaraka. According to some accounts, Pradyumna was an incarnation of Kama, the god of love.
Pradyumna was son of Lord Krishna and 61st grandson of Adinarayan. His mother was Rukmini, whom Lord Krishna got from her father Bhimkashen Narayan. He was the version of God Kamdev. In the Treta Yuga, Kamdev was burnt by Shiva when he became a barrier to Shiva's meditation. Shiva blessed Kamdev's distraught wife, Rati and promised her that in his next birth Kamdev will be a part of Krishna and Rati will be the daughter of Bhimkaraya and that she will marry him.
Pradyumna is also a name of the Hindu god Vishnu. He is one in 24 Keshava Namas (names), praised in all pujas. It is also the only name in Sanskrit with all the 3 letters joint.
The Harivamsa describes intricate relationships between Krishna Vasudeva, Sankarsana, Pradyumna and Aniruddha that would later form a Vaishnava concept of primary quadrupled expansion, or avatar.