was he involved in the military ?
Yes, Hamilton and other King's College students joined a New York volunteer militia company called the Corsicans
Alexander Hamilton
Hamilton and other King's College students joined a New York volunteer militia company called the Corsicans, later renamed or reformed as the Hearts of Oak.
who were the authors of the federalist and what was the purpose of writing it It was written by Alexander Hamilton, James Madison, and John Jay under the collective pseudonym "Publius" to promote the ratification of the United States Constitution. what is it about ? The authors of "The Federalist" intended to influence the voters to ratify the Constitution. In Federalist No. 1, they explicitly set that debate in broad political terms:It has been frequently remarked, that it seems to have been reserved to the people of this country, by their conduct and example, to decide the important question, whether societies of men are really capable or not, of establishing good government from reflection and choice, or whether they are forever destined to depend, for their political constitutions, on accident and force. how is it used in the judicial system ? They have been applied on issues ranging from the power of the federal government in foreign affairs, to the validity of ex post facto laws. where was the writer born ? UNANSWERABLE talk about the first writers educational qualification ? He received private tutoring at King's college and  with  four other undergraduates formed an unnamed literary society that is regarded as a precursor of the Philolexian Society.
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Alexander Hamilton [SEP] Early military career
In 1775, after the first engagement of American troops with the British at Lexington and Concord, Hamilton and other King's College students joined a New York volunteer militia company called the Corsicans, later renamed or reformed as the Hearts of Oak. He drilled with the company, before classes, in the graveyard of nearby St. Paul's Chapel. Hamilton studied military history and tactics on his own and was soon recommended for promotion. Under fire from HMS "Asia", he led a successful raid for British cannons in the Battery, the capture of which resulted in the Hearts of Oak becoming an artillery company thereafter.