Theology is studying the religious beliefs.

Natural theology is information based on facts and oberservations

Revealed Theology is based on revelations and works of faith.

The law of contradiction explains that a thing can not be both true and untrue at the same time, which is different from a paradox. It is a main part of the reasoning and deductive process involved in Scholasticism.

Scholasticism is a way type of thinking or belief, that logic is used to understand things, from normal interactions to religion. It primarly focuses on using reasoning and inference to solve problems.

The problem of evil is the difficulty in explain how evil exists with the presence of an all good and all powerful and knowing god. It is a key argument against religion and a source of much controversy.

Thomas Aquinas believes that love is an act of free will. God will eterenally love you but how you choose to react to that love is your own choice. You can return it with love or choose not to. Love is essentaily the prime virtue and should be sought at all times but it is your own choice to do so.

Five Ways.
The Argument from Motion: Everything is in motion and that motion is caused by something. We can link this motion backwards until we arrive at the first mover, who must be unmovable. 

The Argument from Efficient Causes: Nothing can exsist prior to itself and everything is caused by something. Therefor there must be a first cause, or it would extend infinitly and nothing would exsist.

Argument from Possibility and Necessity: Every being is a contingent being and has a time and reason to exist. But this is not at all times, so there could be a time where nothing exsisted. But if there was nothing then, nothing could exsist after taht point. Therefore not every being is a contingent being, something must have created other beings and not recieved its own being.

Argument from Gradation of Being: Everything has Graduation some better or worse. There is a maximum of a thing, something is hotter, more close to hottest. The maximum of any one thing casuses all those things. There must be some maximum things taht has caused all other maximum things, god.

Argument from Design: Natural things are not random and most of them lack knowledge. Therefor they are directed by some thing. Therefor something directs all things, this is God.

Argument of Design is weakest. It begins with the assumption that all natural things are not random, when in fact they could be so. The intricacy or detail of a thing is not reason for it to not be random, it merely decreases the chances of it being so. Though you may deem it unlikely that all things are not random, it is still an inaccurate assumption to base the existence of a god upon, when all things could function without the god to direct them, merely through chance arriving at a purpose or goal.

The Traditional Juedo-Christian God generates the concept of God because it presents him as all good and all powerful, which would result in him eliminating all evil. Thomas approaches this by saying that God must create free moral agents, who he can't influence or they would not be free moral. Humans are naturally tended to become corrupted, a concept of original justice. Finally he says that the existence of evil is a mystery that humans can not understand. this approach seems weak to me as it does not solve the question, merely shoves the issue to faith.

Aristtole argues that happiness is a virtue obtained, something that is acquired throughout one's life. Happiness is a measure of how you lived your life, it can not be gained or lost in moments. The Hedonists argued that happiness was only momentary, that the moment was all that mattered. Do what gives you joy, nothing else matters. I think that Aristotle's idea is superior. The hedonist view resulsts in all those stoires about people who have everything but are not truely happy. The Aristotle view results in those that are poor and have nothing.