There are two main subgroups within Celtic: The Goidelic subgroup includes Irish and Scottish Gaelic and Manx, the language of the Isle of Man which is now extinct; the Brythonic subgroup includes Welsh, Cornish and Breton.
It was estimated in 1981 that there were about 500,000 Welsh speakers, a decline from about 1 million in the early 20th century. There are probably no Welsh speakers who do not also speak English, but many use Welsh almost exclusively in their everyday home lives, especially in the North of Wales, where the language is far closer to standard literary Welsh than the language of South Wales.
At the time of the Roman invasions, before the English language existed, Welsh and the other Celtic languages were spoken in parts of Britain. Germanic tribes invaded the island from the 5th century onward, and the Celts were mainly forced out of England into the area now called Cornwall and into the countries which became Wales, Ireland, Scotland and Brittany. Ironically, the name 'Welsh' comes from an Anglo-Saxon word meaning "stranger". The native Welsh name for the language is "Cymraeg".
The principality of Wales had Welsh as its official language, but Llywelyn ap Gruffydd, the last ruling prince of Wales, was killed in 1282 by the forces of the English king Edward I. Edward declared himself conqueror of Wales and named his new-born son the Prince of Wales. The English rulers gained increasing control over Wales, until in 1536, the Act of Union established English as the language of the courts in Wales and banned Welsh speakers from official employment. During the 19th and early 20th centuries, Welsh was banned in schools, but kept alive by Nonconformist Christian chapels throughout Wales. In the later 20th century, renewed protest against the subjugation of the language led to the first Welsh-medium state schools, the establishment of a Welsh-language television station and the first court cases heard entirely in Welsh.
Contrary to popular opinion, Welsh is not a "hard" language to speak. It has complexities such as the mutation system, which dictates that certain letters at the beginning of words change in certain circumstances. You only have to look at English spelling, though, to realise that no language is "easy" to a non-native speaker. Another popular preconception about Welsh is that it is outdated and old-fashioned. This is also untrue. It is a language which is keeping up with modern technology. Words for "internet" and "disk-drive" exist, for example. (Although admittedly not many people use them!)