In the study of God (theology), what is the difference between a contradiction, a paradox, and a mystery? Why is the Trinity a mystery and not a contradiction?

The doctrine of the Trinity is a crucial ingredient in our Christian faith because it explains who God is, what He is like, how He works, and how He is to be approached. Its truth has profound practical implications for the Christian life:

(1) In the completion of our salvation.
(2) In our worship.
(3) In our prayer.
(4) In our understanding of love and unity.