(1) I worked hard.

(2) I hardly worked.

(3) I worked hardly.

(4) Hardly, I worked.

(a) The sentences (1) and (3) imply that I worked hard, but sentence (2) says I didn't work at all. Would you please confirm if my understanding is correct?

(b) What is the meaning of sentence (4)?

Only the first two are used, and they mean very different things (as you have already pointed out) because "hard" and "hardly" have very different meanings in spite of the similarity in spelling.

"hard" means "diligently", "industriously". It tells how you worked. It tells the manner in which you worked.
"hardly" means "almost not at all" (not "not at all"), "little", "not much at all". It tells how much you worked. It tells the degree to which you worked.

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Thanks, CalifJim.

May I conclude sentences (3) and (4) are grammatically incorrect?. Since an adverb can be used in different positions of a sentence, I thought 'I hardly worked' and 'I worked hardly' have the same meaning.
The adverb "hardly" is not positioned so freely as other adverbs. It is placed just before the verb. The same is true for its synonyms "scarcely" and "barely". Note that these are adverbs of negative polarity and that "not" itself has the same property. It, too, is placed just before the verb. "almost" -- of positive polarity -- also has this property.

We don't say any of these:

I did work not.
I understood [hardly / scarcely / barely] the explanation.
I won almost the race.

We say:

I did not work.
I [hardly / scarcely / barely] understood the explanation.
I almost won the race.


The elements of negative polarity can also be placed at the beginning of the sentence, but in that case they trigger inversion, just as other negatives do.

"Hardly had I begun to study when the phone rang." (not "Hardly I had begun ...")

Thanks, CalifJim. Now I understood the concept.
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I would just like to point out that while in the above example, it's true that "hardly" likely means "to almost no degree," it can and theoretically could mean "not at all." I would venture to say that usually when it is used in the "not at all" sense, there is a certain accompanying tone of voice (sort of sarcastic), or the context makes it clearer.

For example, someone could ask, "Did you work?" One could reply, "Ha! Hardly." (The "ha" is added to emphasize the tone of this reply.) In this case, you are using "hardly" in the sense that you did not work at all. One could also reply, "We hardly worked at all," and in this case you are unambiguously using it in the sense that CalifJim mentioned.

Another example sentence of "hardly" being used in the "not at all" sense would be, "This is hardly the appropriate time to discuss such matters." In this case, the sarcastic tone of voice is not needed, as the context makes the meaning clear. If the sentence "I hardly worked" were to use "hardly" in the "not at all" sense, a sardonic tone would be required, ie "I hardly worked." The proper tone and emphasis on the words is difficult to convey in writing, though, so if one were to encounter that sentence in the wild with no context to indicate otherwise, the meaning is most likely the one referred to by CalifJim.