Many thanks, Christopher, that is very clear. My incomplete neophyte understanding of the data constructs involved meant I would never have seen that. I shall give this a go first thing.

Cheers!

I make up a set up data in the form of a csv file for working with, like the one in your example:

fileText = "Country,Date,Value
  Albania,01/01/2005,345.65
  Albania,01/01/2006,453.45
  Bangladesh,01/01/2005,34.65
  Bangladesh,01/01/2006,45.45";

Then I make an 'a', using SemanitcImportString to simulate reading your file:

a = SemanticImportString[fileText, {"Country", "Date", "Number"}]

What you are now working with is a Dataset:

a[All, {"Date", "Value"}]

What DateListPlot wants is separate timeseries, one for each Country:

a[GroupBy["Country"], All, {"Date", "Value"}]

DateListPlot[a[GroupBy["Country"], All, {"Date", "Value"}]]