It is incorrect to think of Scotland as a wholly Celtic country. Since the first millenium BC, Scotland has been a place of multiple languages and this tradition continues today. First of all it was Pictish and British; then Gaelic, Norse and Scots came and today it's English, Scots and Gaelic. Nearly all of Scotland was once Gaelic speaking except Orkney, Shetland and Caithness which had a variety of Norse until recent times and East Lothian which was settled by the Angles. Galloway had a Gaelic community which became separated from the Gaelic speaking Highlands and Gaelic was still in use until about the 17th century in Galloway. "Poets, scholars and writers in Lowland Scotland up until the 16th century readily acknowledged Gaelic to be the true and original Scottish language. For Walter Kennedy 'it suld be al trew Scottis mennis lede': ('Flyting with Dunbar' c.1500)" : section quoted from "Gaelic: a past and future prospect", Kenneth Mackinnon. Gaelic is a Celtic language, like Irish.
Other notable reads include anything by the late Prof Kenneth Jackson, particularly "A Celtic Miscellany", any of John Prebble's books (ie "1000 years of Scottish History") or Nigel Tranter ("The Story of Scotland") To the Gaelic Homepage