Below are very brief presentations of these arguments. They are meant to be simplified so that the general thrust of each argument can be understood very quickly. You can search any one of these arguments on Youtube for a more thorough treatment.
Cosmological Argument – God is the best explanation for the beginning of the universe.
Moral Argument – God is the best explanation for objective moral values and duties.
Evidence for the Resurrection – The resurrection of Jesus is the best explanation of the historical evidence.
Argument from Contingency – God is the best explanation for why anything exists rather than nothing.
Argument from Meaning – Our lives can only have meaning if God exists.
Argument from Origin of Life – God is the best explanation for the origin of life.
Argument from Knowledge (difficult) – God is the best explanation for our ability to know anything (warning: this argument is very abstract).