Origins
The word 'notice' enters English from Old French 'notice' (information, intelligence, knowledge), which derived from Latin 'nōtitia' (a being known, fame, knowledge, acquaintance). The Latin noun traces to 'nōtus,' the past participle of 'nōscere' — an earlier form 'gnōscere' — meaning 'to get to know, to become acquainted with, to learn.' This verb descends from Proto-Indo-European *ǵneh₃- (to know), one of the most fundamental roots in the Indo-European language family.
The PIE root *ǵneh₃- produced two great branches of 'knowing' words: one through Latin and one through Germanic. The Latin branch gives English 'notice,' 'notion,' 'note,' 'notify,' 'notorious' (known for bad reasons), 'noble' (well-known), 'cognition,' 'recognize,' 'incognito' (not known), 'ignorant' (not knowing, from 'in-' + 'gnārus'), and 'narrate' (from 'gnārus,' knowing). The Germanic branch gives 'know,' 'knowledge,' 'acknowledge,' 'can' (originally 'to know how'), and 'cunning' (originally 'knowing').
In Latin, 'nōtitia' had a range of meanings: it could mean fame (being known by many), acquaintance (knowing someone personally), or knowledge (the state of having learned something). It was the abstract noun of knowing — the condition of being in a state of knowledge. When it entered Old French, the emphasis shifted toward practical information: a 'notice' was a piece of intelligence, something that brought you into the state of knowing.
Middle English
Middle English borrowed the word in the fifteenth century, and it quickly developed multiple senses that persist today. 'Notice' as attention or observation ('she took notice of his absence'); 'notice' as a formal written announcement ('a notice on the wall'); 'notice' as advance warning ('two weeks' notice'); and 'notice' as a review or critique ('the book received favorable notices'). All these senses orbit the central idea of bringing something to someone's awareness — making the unknown known.
The verb 'to notice' (to become aware of, to observe) developed slightly later, in the mid-sixteenth century. Its casual, everyday quality belies its deep etymological roots. When you 'notice' something, you are — in the word's deepest sense — coming to know it, entering into acquaintance with it.
The legal sense of 'notice' is particularly important. In law, 'notice' means knowledge of a fact that would cause a reasonable person to inquire further. 'Constructive notice' is a legal fiction: if information was publicly available (recorded in a land registry, for instance), you are deemed to have 'notice' of it whether you actually knew it or not. 'Actual notice' means you really did know. The distinction between constructive and actual notice is one of the most consequential in property law, contract law, and due process.
Proto-Indo-European Roots
The family of related words is enormous. 'Notorious' originally meant simply 'well-known' — the negative connotation (known for bad things) developed later. 'Noble' comes from Latin 'nōbilis' (knowable, well-known, famous), from the same root; aristocratic nobility was originally about public recognition, not moral character. 'Cognition' comes from 'cognōscere' (to get to know thoroughly, with the prefix 'co-' intensifying the root). 'Recognize' is to know again ('re-' + 'cognōscere'). All of these are branches of a single PIE root that meant simply 'to know' — the most basic mental act that language can name.