There are several useful publications on the history of banking and most of the main bank groups operating in Scotland: Bank of Scotland, The Royal Bank of Scotland, Clydesdale Bank, and Lloyds TSB. Each bank is the result of a number of amalgamations over the last 300 years. General reference books on the subject include:
Checkland, S., Scottish Banking, A History, 1695-1973 (Collins, 1975)
Cameron, Alan, Bank of Scotland 1695-1995: a very singular institution (Mainstream Publishing, 1995)
Durie, A J. ed., The British Linen Company 1745-1775 (Scottish History Society, 1996)
Kerr, A. W., History of Banking in Scotland (D Bryce & Son, 1884)
Malcolm, C. A., The Bank of Scotland 1695-1945 ([1948])
Malcolm, C. A., The History of the British Linen Bank, 1746-1946 (Edinburgh, 1950)
Moss, Michael & Anthony Slaven, From ledger book to laser beam: a history of the TSB in Scotland, from 1810-1990 (Trustee Savings Bank Scotland, 1992)
Moss, Michael & Iain Russell, An Invaluable Treasure: A History of the TSB (Weidenfeld & Nicolson, 1994)
Munn, C., The Scottish Provincial Banking Companies, 1747-1864 (John Donald, 1981)
Orbell, J. & A. Turton, British Banking: A Guide to historical records (Ashgate, 2001)
Rait, Robert S., The History of the Union Bank of Scotland (Glasgow: 1930)
Saville, R., Bank of Scotland: A History, 1695-1995 (Edinburgh University Press, 1996)
Tamaki, Norio, The Life Cycle of the Union Bank of Scotland 1830-1954 (Aberdeen University Press, 1983)
If you are researching the history of the Bank of Scotland or The Royal Bank of Scotland (or one of their constituents) look at the respective websites: <https://www.lloydsbankinggroup.com/who-we-are/our-heritage/our-companies.html> [accessed 24 April 2024] for the Bank of Scotland and <https://www.natwestgroup.com/heritage.html> [accessed 24 April 2024] for the Royal Bank of Scotland. The National Archives website <http://discovery.nationalarchives.gov.uk > [accessed 24 April 2024] will help you locate the archives services which hold records of other banks.