In our mythology, we come across three prominent persons named Raama. Usually, the name Raama generelly refered to means that Raama of Raamaayana, a kshathriya, son of Dasharatha. This Raama was famous for killing the demon Dashakantha(Raavana). Another Raama was prior to him and existed even later . He was Parashuraama, a Braahmana, son of sage Jamadagni. This Raama was famous for exterminating the Kshathriya clans twenty one rounds. The third Raama was Krishna's half-brother, so he too was a kshathriya. He was known as Balaraama. Thus, Except Raama of Raamaayana, the other two Raamas are generally referred to as Parashuraama and Balaraama. But the context will clarify which Raama is meant in the reference.
All the three Raamas are incarnations of Vishnu. The order of their incarnations is first - Parashuraama, second - Raama and third - Balaraama. Their general description to distinguish among them is made as Bhrigu-Raama, Raghu-Raama and Yadu-Raama. The prefixed epithets indicate their dynasties.
Raama of Raamaayana was a great hero of the nation. Besides his being an incarnation of Vishnu, his noble character made him a moral ideal person for Indians. Details about him can be seen in the link Raamaayanam.
Details about Parashuraama are given in link Parashuraama
Details about Balaraama are given in link Balaraama
"After praying to Naaraayana, Nara, Sarasvathi and Vyaasa, then one should read the Jayam."
DEDICATED TO MY DEAR NIECE VYSHNAVI KRISHNA