Short answers, pulled from the story.
Phonology is the branch of linguistics that studies how languages organize sounds or sign components to encode meaning. Phonetics concerns the physical production, acoustic transmission, and perception of those sounds; phonology describes how they function within a given language or across languages. For many linguists, phonetics belongs to descriptive linguistics and phonology to theoretical linguistics.
The French linguist A. Dufriche-Desgenettes coined the word phoneme in 1873, proposing it at a meeting of the Société de Linguistique de Paris on the 24th of May as a one-word equivalent for the German term Sprachlaut. The Polish scholar Jan Baudouin de Courtenay then shaped its modern usage in a series of lectures in 1876-1877.
The Sound Pattern of English, published in 1968 by Noam Chomsky and Morris Halle, is the foundational text of generative phonology. It proposed that phonological representations are sequences of segments built from binary distinctive features, and it introduced ordered rules that transform underlying representations into surface pronunciations. Its influence shifted the field's focus toward segments and away from the syllable.
Optimality theory is a framework developed by Alan Prince and Paul Smolensky at the LSA summer institute in 1991. It holds that languages select a pronunciation by choosing the form that best satisfies a ranked list of constraints, where a lower-ranked constraint can be violated to obey a higher-ranked one. John McCarthy and Alan Prince extended the approach to morphology, making it a dominant trend in the field.
The Ashtadhyayi, a Sanskrit grammar by Pāṇini dating to the 4th century BCE, contains the earliest known systematic investigation of a language's sounds. Its auxiliary work, the Shiva Sutras, provides an inventory of Sanskrit phonemes along with a notational scheme used throughout the main text.
Phonological principles apply to sign languages because they are designed as general analytical tools, not ones specific to speech. In American Sign Language, signs contrast on dimensions such as hand shape, as seen with CAR and WHICH, and location, as seen with APPLE and ONION. These contrasts function as minimal pairs, directly analogous to sound contrasts in spoken languages.