almost

Very close to, but not quite.

Almost all people went there.

We almost missed the train.

Up to, except for a negligible set (where negligible is not universally but contextually defined).

almost all

almost no

Up to, except for a negligible set (where negligible is not universally but contextually defined).

almost everywhere

almost nowhere

Something or someone that doesn't quite make it.

In all the submissions, they found four papers that were clearly worth publishing and another dozen almosts.