Who were the republicans? what caused their formation? which groups composed this party, and what was the party's platform?

The Republican Party (abbrev. GOP for "Grand Old Party") is one of the two oldest parties in the American political system. The other being the democratic party. It was started in the mid 19th century (~1854) by anti-slavery activists. The party has traditionally been hallmarked by conservativism, whereas the democratic party is hallmarked by more modern liberalism. The democratic and republican parties that we know today are not necessarily the same philosophical parties that they were throughout the early part of the 20th century. The republican party was the dominate political party in the US until 1932, and included presidents Abraham Lincoln and Teddy Roosevelt. 

The term "economically liberal and socially conservative" was coined to describe the type of economic and social balance sought by the party. Economically, the republican party favors limited government, the free market system, and a fertile capitalistic environment. Socially the party rejects the liberal opinions of it's contrasting party.

The party was formed by a group of antislavery activists, ex-Whigs, ex- Free Soilers, and modernizers. The republican party was formed in response to the Missouri Compromise, which would have allowed for further northern expansion of slavery, something that was seen as a great and terrible evil. (Unlike the Southern Democrats.) They opposed slavery and the plantation system and pushed for a system of labor and business that would allow men to grow and capitalize small businesses. 

There are tons more resources about the party system online, many of which will give a much clearer picture of the parties formations, but the long and short of the two-party system is that it rose up from the end of the slavery system in the United States and has continued to grow and change into what we now consider modern republicanism.