The personality of God is a mystery. Its is far beyond human reasoning or comprehension. However God manifested Himself to man in the form of three personalities namely The Father, The Son and The Holy Spirit. How could this be when we say God is one.

Starting from the beginning, the bible says "God created man in His own image"
Genesis: 1. 27. So God created man in his own image, in the image of God created he him; male and female created he them.

Man was created as a tripartite being in the nature and likeness of God, that is man is a spirit, soul and body. All these three distinct consciousness is what makes a man. If one of these personalities is removed then man cannot be man again yet with these three distinct personality working harmoniously we have one person. for instance if the spirit leaves the body the man is dead, when the soul is removed then man becomes like an animal( when the soul is corrupted man becomes insane behaving like an animal) and also when the body is destroyed man ceases to exist on this side of the great divide (the physical world). So these three entities must be complete and present to have human being.
So also God is one but with three district yet unified personalities.

1 Thessalonians: 5. 23. And the very God of peace sanctify you wholly; and I pray God your whole spirit and soul and body be preserved blameless unto the coming of our Lord Jesus Christ. - Bible Offline

For those who don't belief in the bible let's take a look at nature.
Take a cup of water and put it in a freezer, what you will get is ice block (a manifestation of water under freezing condition). Bring out the block and let is stay under room temperature. It will melt back into water( under that condition), if the same water is heated well above room temperature it turns into steam as it evaporates. Collect the vapour and you have your water back. So the same water in solid, liquid and gaseous states yet the same water.
The question is 'how many 'water' do we have in that illustration ?' I leave the answer to the power of your imagination.

This over simplified illustrations may not adequately describe the mystery of the Triune God but at least they gave insights into it as far as human imaginations can bear.

To deny the doctrine of trinity is to deny the existence of man & nature.

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Trinity- 3 in one- Triune... Evident @ the baptism of Jesus Christ,