The movement of Celts from north of the Alps into the Mediterranean lands in the period from about 400 BC is amply documented by Greek and Roman historians writing several centuries after the events. [...] Our two principal sources [are] Polybius (c.204-122 BC) and Livy (59 BC-AD 17).
Celtic language studies really began in Oxford at the end of the seventeenth century with the researches of Edward Lhuyd.p. 48
Lhuyd [...] envisioned an initial colony of invaders from Gaul moving into Britain, but later being forced out, to Scotland and Ireland, as a second wave of invaders from Gaul moved in. In Ireland they mixed with the indigenous Scotti, who had earlier arrived from Spain and some of whom later crossed into what was to become Scotland.p 50
[...] it has been conventional to divide [the insular Celtic languages] in two groups, Q-Celtic or Goidelic and P-Celtic or Brythonic. The distinction is made on the basis of the pronunciation (and thus of the spelling) of the qu sound. In Q-Celtic it remains as the hard q- or later k-, whereas in P-Celtic it softens to p-; thus in Irish 'four' is cethir and in Welsh pedwar. [...] Q-Celtic is spoken in Ireland, the Isle of Man, and western Scotland, while P-Celtic is spoken in Brittany and Wales and was until c.1800, also spoken in Cornwall. It also seems to have been the language of the rest of Britain before its gradual replacement.
For more than 1,000 years following the collapse of the Roman world in the West, the concept of the Celts real or imagined seems to have passed out of consciousness.
p 112
It was, however, the Scottish historian George Buchanan who was to introduce the word 'Celt' into the discussion in his Rerum scoticarum historia published in 1582. Buchanan believed that the Celts originally lived in northern Italy, southern and central France, and western Iberia. In this he was presumably basing himself closely on Classical texts. From Iberia, he believed, the Celts migrated to Ireland, and subsequently some of them (as Scotti) settled in the west of Scotland.
In 1703 Pezron published his L'Antiquité de la langue et de la nation des Celtes. What he offered was, in reality, a new origin myth that provided the French in general, and the Bretons in particular, with grand and impressive genealogy [Noah].
p 118
[The] Scot James Macpherson [...], between 1760 and 1763, published a series of poems ascribed to Ossian, son of Fingal, a semi-legendary Gaelic bard. [...] His sources, he claimed, were two manuscripts 1200 or 1300 years old.
p 119
In 1838 a young Breton aristocrat Vicomte Hersart de la Villemarqué published a collection of ballads Barzaz-Breiz (Songs of Brittany), which he had gathered among the Breton peasantry.