Definition of quickly adverb from the Oxford Advanced American Dictionary

      

    quickly

     adverb
    adverb
    NAmE//ˈkwɪkli//
     
     
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  1. 1fast She walked quickly away. We'll repair it as quickly as possible. The last few weeks have gone quickly (= the time seems to have passed quickly).
  2. 2soon; after a short time He replied to my letter very quickly. It quickly became clear that she was dying. note at Which Word?quick / quickly / fast Quickly is the usual adverb from quick:I quickly realized that I was on the wrong train. My heart started to beat more quickly. Quick is sometimes used as an adverb in very informal language, especially as an exclamation:Come on! Quick! They’ll see us!Quicker is used more often:My heart started to beat much quicker. The quicker I get you away from here, the better. Fast is more often used when you are talking about the speed that someone or something moves at:How fast can a cheetah run? Can’t you drive any faster? You’re driving too quickly.There is no word fastly.soon
See the Oxford Advanced Learner's Dictionary entry: quickly