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Latter means the second of two and is contrasted with former
He studied French and German, but the former language he speaks very well, but the latter one only imperfectly.
Lattest means the most recent,the last up to the present.
Have you read John Scribbler's latest book?It was written in three weeks and published two days ago.
Last have the meaning final
The T empest was probably the last play that Shakespeare wrote.
It also has the meaning previous
I think this recent book is better than his last one.
Last week/year/month...........................