Inversion 1: After Negative or Limiting Adverbs

Inversion happens in English for emphasis, dramatic purpose or formality. This type of inversion uses negative and limiting adverbs these are a group of adverbs which limit the meaning of a verb or make it negative. Examples are:

never, hardly, no, rarely, seldom, little, barely, no sooner...than, in no way, under no circumstances, nowhere, not (+time), (only+ time). This is not a complete list.

To invert a sentence move the adverbial to the beginning of the sentence and invert the subject and auxiliary verb:

‘I had never met someone so interesting.’ becomes ‘Never had I met someone so interesting.’
'He won't often go to work.' becomes 'Not often will he go to work'
'You should not leave this room for any reason' becomes 'Under no circumstances should you leave this room.'
'She hasn't seen him anywhere.' becomes 'Nowhere has she seen him'

Notice that if the auxiliary verb is negative in the first sentence, it becomes affirmative in the inverted sentence and the 'not' moves to the front.

In cases where the tense does not use an auxiliary verb in the affirmative, such as the present simple or the past simple, one must be added. 

Present Simple:
‘I rarely go outside.’  becomes  ‘Rarely do I go outside.’
'They don't ever know what to do' becomes 'Never do they know what to do.'
'She almost never loses' becomes 'Scarcely does she lose.'

Past Simple: (Notice how the verb changes from past tense to infinitive)
‘She seldom worked very hard.’ becomes ‘Seldom did she work very hard.’
'We never went to the shopping centre.' becomes 'At no time did we go to the shopping centre.'
'He didn't react at all.' becomes 'In no way did he react.'

Some negative or limiting adverbials require you to complete a whole clause before the inversion takes place. 

‘I didn’t know what to do until I saw what had happened.’ becomes ‘Not until I saw what had happened did I know what to do.’

In this case, ‘Not until I saw what happened’ is the adverbial clause. The inversion takes place after this, in the main clause. This happens with 'Not +time' and 'Only + time'.

Not + until / before + clause
Only + when / as / after / while / once + clause

Other examples are:

'Only when they met again did he tell her'
'Not before he admitted the truth did they let him go'
'Not since Paris had they seen such a beautiful sunrise.'
'Only now could he see how wonderful a car it was.'

'Hardly' puts the inversion in the adverbial clause. It uses 'than' and 'when' to connect with the main clause.

‘Hardly had I got home than the dog started barking.’
'Hardly had he got into the bath when the phone rang.’

Little did they know means they didn't know. The subject can be changed. Little can also be combined with nouns to show a lack of something, such as food or time.

‘Little did they know that he had stolen all of their money.’ (They didn't know he had stolen all of their money)
'Little did he know that they would never meet again.' (He didn't know that they would never meet again.)
'Little time did they have to explain.' (They didn't have time to explain)
'Little patience does she have on a good day!' (She doesn't have any patience on a good day!)