The City of Glasgow refers to the formal title and redefinition of Glasgow, Lanarkshire, Scotland following the changes that occurred in 1996 leading from the Local Government etc. (Scotland) Act 1994. Prior to that date, and particularly before 1975, Glasgow was a parish within the county of Lanarkshire, as well as a city. Since most records of a genealogical nature are based on the parish structure, Glasgow is a far better page to consult than this one.
The description in the following Wikipedia article that starts from "Glasgow City became one of the newly created single tier local authorities in 1996..." explains the geographical alterations that went with the changes in the form of government.
Glasgow City Council became one of the newly created single tier local authorities in 1996, under the Local Government etc. (Scotland) Act 1994, with boundaries somewhat different from those of the City of Glasgow district of the Strathclyde region: parts of the Cambuslang and Halfway and Rutherglen and Fernhill areas were transferred from the city area to the new South Lanarkshire council area.
The district had been created in 1975 under the Local Government (Scotland) Act 1973 to include: the former county of the city of Glasgow and a number of areas previously within the county of Lanark: Cambuslang (Central and North, and South lying outwith East Kilbride), Rutherglen (including the burgh of Rutherglen), part of a Carmunnock area (that lying outwith East Kilbride) and Baillieston, Carmyle, Garrowhill, Mount Vernon and Springboig.
Refer to Glasgow for references for parish records, vital records since 1855, censuses, cemetery records, poor law records and further sources of information.