The American slasher that was formalized and calcified in the late '70s/early '80s did not come out of nowhere; in fact, some of its narrative/structural antecedents date as far back as the '20s and '30s. Most notably, the subgenre draws from the Italian giallo of the '60s/'70s and the 1960 watershed double-threat of Psycho (U.S.) and Peeping Tom (U.K.). Here is my highly subjective, constantly fluctuating canon/genealogy/watch-log of the subgenre.
Required reading: Carol J. Clover, Men, Women, and Chain Saws (1992)
Bro banter aside, this episode of Talk is Jericho featuring Eli Roth and editor Mark Goldblatt is hugely informative. Also essential: Going to Pieces: The Rise and Fall of the Slasher Film.
Subject to change. Recommendations welcome.