school (n.1) Look up school at Dictionary.com
"place of instruction," Old English scol, from Latin schola "intermission of work, leisure for learning; learned conversation, debate; lecture; meeting place for teachers and students, place of instruction; disciples of a teacher, body of followers, sect," from Greek skhole "spare time, leisure, rest ease; idleness; that in which leisure is employed; learned discussion;" also "a place for lectures, school;" originally "a holding back, a keeping clear," from skhein "to get" (from PIE root *segh- "to hold, hold in one's power, to have;" see scheme (n.)) + -ole by analogy with bole "a throw," stole "outfit," etc.

The original notion is "leisure," which passed to "otiose discussion" (in Athens or Rome the favorite or proper use for free time), then "place for such discussion." The Latin word was widely borrowed (Old French escole, French école, Spanish escuela, Italian scuola, Old High German scuola, German Schule, Swedish skola, Gaelic sgiol, Welsh ysgol, Russian shkola). Translated in Old English as larhus, literally "lore house," but this seems to have been a glossary word only.

Meaning "students attending a school" in English is attested from c.1300; sense of "school building" is first recorded 1590s. Sense of "people united by a general similarity of principles and methods" is from 1610s; hence school of thought (1864). School of hard knocks "rough experience in life" is recorded from 1912 (in George Ade); to tell tales out of school "betray damaging secrets" is from 1540s. School bus is from 1908. School days is from 1590s. School board from 1870.
school (n.2) Look up school at Dictionary.com
"group of fish," c.1400, from Middle Dutch schole (Dutch school) "group of fish or other animals," cognate with Old English scolu "band, troop, crowd of fish," from West Germanic *skulo- (cognates: Old Saxon scola "troop, multitude," West Frisian skoal), perhaps with a literal sense of "division," from PIE root *(s)kel- (1) "to cut, divide" (see scale (n.1)). Compare shoal (n.2)). For possible sense development, see section from Latin secare "to cut."
school (v.1) Look up school at Dictionary.com
"to educate; to reprimand, to discipline," mid-15c., from school (n.1). Related: Schooled; schooling.
school (v.2) Look up school at Dictionary.com
"collect or swim in schools," 1590s, from school (n.2). Related: Schooled; schooling.