Contract verbs
 
Contract verbs look more difficult than they really are. Like so many things in languages, everyday usage and fluency of speech dictate many "irregularities". So, whereas
παιδεύω, παιδεύεις , παιδεύομεν ....
λύω, λύει, λύετε......

sounded good to ancient Attic Greek ears,
ποιέω, ποιέει, ποιέετε...
τιμάω, τιμάεις, τιμάομεν....
πληρόω, πληρόομεν, πληρόουσιν

obviously did not.
So, for fluency and ease of speech - ancient Greek was a spoken language after all - the verb endings combined with the a/e/o of the stem to form what look like irregular endings but are in fact regular endings in disguise. And we speak of "contract" verbs in -a, in -e or in -o according to the end vowel of the stem.
 
1. Verbs in
2. Verbs in
3. Verbs in -ο
 
 
 
1. Contract verbs in -ε-   Contractions
Present Indicative
 φιλέω => φιλ   + ω  =>
 φιλέεις
 φιλέει
=>
=>
φιλεῖς
φιλεῖ
  + ει  => εῖ
 φιλέομεν => φιλοῦμεν   + ο  => οῦ
 φιλέετε => φιλεῖτε   + ε   => εῖ
 φιλέουσιν   => φιλοῦσιν   + ου => οῦ
Imperative
 φίλεε => φλει   ε + ε => ει
 (φιλέετε => φιλεῖτε)    
Infinitive
 (φιλέειν => φιλεῖν)    
 
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2. Contract verbs in -α-   Contractions
Present Indicative
 βοάω => βοῶ   + ω =>
 βοάεις
 βοάει
=>
=>
βο͂ς
βο
+ ει =>
 βοάομεν => βοῶμεν   + ο =>
 βοάετε => βοᾶτε   + ε =>
 βοάουσιν => βοῶσιν   + ου =>
Imperative
 βόαε => βόα   α + ε => α
 (βοάετε => βοᾶτε)   
Infinitive
 (βοάειν => βοᾶν ) ! attention ! NO ι subscript
 
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3. Contract verbs in -o-   Contractions
Present Indicative
 πληρόω => πληρῶ   + ω =>
πληρόεις
 πληρόει
=>
=>
πληροῖς
πληροῖ
  + ει => οῖ
πληρόομεν => πληροῦμεν   + ο => οῦ
 πληρόετε => πληροῦτε   + ε => οῦ
 πληρόουσιν => πληροῦσιν   + ου => οῦ
Imperative
 πλήροε => πλήρου   ο  + ε  =>  ου
 (πληρόετε => πληροῦτε)    
Infinitive
 (πληρόειν => πληροῦν) ! attention ! ον   NOT  οῖν
 
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