Arianism -A view that subordinates Jesus to a God that is lesser than Jehovah.  Also a multi-God belief system. 
 

Modalism  -Is the view that God is one person, one God. While I am not a modalist, I still  consider modalist my brothers,  since modalist believe that Jesus is God, and they  believe in one God. Which are two of  the necessary doctrines of Christianity.  I still do not believe that this is the proper view of the God-head. 

Why? Because modalism ignores the distinctness of each person in the Godhead. 

Which brings me to the fourth view of the Godhead. and that is 
Trinitarianism believes that God is one God and three persons Trinitarians believe that God is one in compound unity. He is one in regard to essence. 
Since our heavenly God is so complex I will try to explain the trinity using an earthly  example that we all understand. 
H20 
H20 if  I were to take a glass of H2O and  pour it into a pot on the stove it would soon turn to steam 
and you could put H2O in the freezer and turn it into ice.  While H2O is one in essence it can be three different things ; ice, water and steam. In fact their is a chemical  reaction called the triple point of Water. It is when H2O can become steam, water, and ice at the same time. 

While I can't show you how God can be three at  one time I have shown you that it is possible to be three at one time. 

Now I will try to show how God is three persons not just three different modes.