We can't understand the mystery of the Trinity, it's normal. It would be necessary to be like God to understand it fully. But thanks to the Holy Bible and to the Holy Spirit, to help us to know the only true God, and Those who He sent : Jesus Christ ( 1 Cor 2 : 10 )
Trinity : a Latin word whose meaning is : one God in three Persons, distinct and inseparable. In German, it's Tri-unit ( Dreieinigkeit ), which is even more expressive. The Father, the Son, & the Holy Spirit are called God in the Bible ( Gen 1 : 1 - Titus 2 : 13 - Acts 5 : 3, 4 )
Most of times in the New Testament, the Father, the Son and the Holy Spirit are mentioned together, sometimes in parallel, sometimes in their mutual relations. That means that in their unit, They are distinct one from the other. When the same man is husband, father, citizen, engaged in such or such profession, member of such or such church, he does several functions, while having only one personality. The Father, the Son and the Holy Spirit have their own activities, They have each one a distinct personality. This is why They can be mentioned together, as in the baptismal formula : « In the name of the Father, of the Son and the Holy Spirit » ( Matthieu 28 : 19 ). If Jesus prayed and if He continues to do it now in glory, that proves that It does not merge with God the Father ; and Jesus said that the Holy Spirit is another Helper. That means there are differences between these three Persons.
( John 14 : 16 Words of Christ ) : « I will ask the Father, and He will give you another Helper, who will stay with you for ever ».
Note the subordination of the Son compared to the Father : it is the Father who sent the Son in the world and not the reverse ( John 8 : 18 ). Note too the subordination of the Holy Spirit : He is sent by the Father and the Son ( John 14 : 26 )
Extract from « PRECIS DE DOCTRINE CHRETIENNE » J.M. Nicole. Thanks to Randriatsara Hajason ( Ankadifotsy A.F.F. ) to lend me the book