TIME:   When did, does, will it happen?
  λε λύω   I loosen, set (the dog) free 
 I am loosening 
 I do loosen 
  Present Tense
  λέλυκα  I have loosened, and here is the result:
      a dog running free
  Present Perfect  
  λλυσα   I loosened    Aorist Simple Past  
  λλυον   I was loosening 
 I used to loosen 
 I started to loosen
 ἐλελύκη  I had loosened 
  (and there was a result)  
 λέ λύσω   I shall set free 
 I shall be setting free 
  Future Tense
 extremely rare in Greek,
   forget it
 I shall have loosened 
  (and there will be a result)  
  Future Perfect  


 Future Tense   often indicated by σ  inserted between stem and ending.
 Past Tenses   are always indicated by a past tense marker, either ε 
(either written or implied, i.e. indicated through lengthening of the initial vowel. Don't worry about that at the moment, we'll get there.)
 Perfect Tenses   verbs starting with a consonant :
παιδεύω duplicate that consonant and insert an ε between the 2:
What's missing now is the perfect marker κ between the stem and the ending (in the active forms only):
     παιδεύω > πεπαίδευκα
>  κεκέλευκα
And a set of special, hybrid endings. We met present perfect forms here.
Pluperfect (Latin:plus-quam-perfectum = more than perfect) being a past tense needs the past tense marker
πεπαίδευκα >πεπαιδεύκη (and a different set of endings of course).
But pluperfect isn't on the menu till half-way through Athenaze II. Thank Zeus for small mercies.