Theology is a combination word. The prefix "theo" comes from the Greek theos (Strong's Concordance #G2316) which can reference the real God or pagan deities. It is used more than 1,300 times in the Greek text that underpins the KJV New Testament. The suffix "logy" (sometimes "ology") means the study of a particular subject. The basic definition of theology, therefore, is the scientific study of God, his attributes and nature, as well as his relationship with the world in general and man in particular.
Covenant theology uses the template of a covenant to understand the structure of the Bible. It asserts that God initially made an agreement with Adam based on works. After Adam sinned, however, a new covenant was established with the "second Adam" Jesus (1Corinthians 15:45 - 49). It also supports the concept that although God has not abandoned His promises to Israel, the fulfillment of them is found in the person and work of Christ.
Dispensational theology maintains that God works with different people, in different ways, during different Biblical history periods. One example of this is the period from God's law at Sinai to Jesus' crucifixion being considered the "age of law." It also considers the "age of grace" to be from the Lord's death to the present. Additionally, dispensationalism maintains God isn't done yet with Israel as his chosen people (as per Romans 11:1).
Liberation theology is one of many ways or lenses through which humans have sought to interpret what the Bible teaches. It most well-known manifestation originated within the Roman Catholic Church in Latin America during the 1960's. This theology focuses on those who are oppressed, poor, or otherwise unjustly treated by economic, political or social structures. It draws on "liberation" themes in Scripture, like the Exodus, to advocate for dramatic social changes.
This theological viewpoint has been criticized by some for sometimes relying on Marxist explanations and principles for the causes of oppression. Others have also criticized it for focusing on human-centered goals rather than a saving faith in the Gospel.
Natural theology attempts to gain understanding about God without and apart from any revelation from him. It maintains that, "humans can attain particular knowledge about God through human reason by observing the created order as one locus of divine revelation" (Pocket Dictionary of Theological Terms). God's existence, for example, is inferred through cosmological arguments and on human experience in general.
Reformed theology grew out of the teachings of John Calvin and Ulrich Zwingli. It emphasizes God's sovereignty and that Christians ought to transform and redeem various areas of human society.
Replacement theology interprets the Bible from the view that the Christian church has completely replaced the physical nation of Israel as God’s chosen people. It asserts that the New Covenant, made through Jesus Christ, completely supersedes the Old Covenant that it believes was made for Jews only. This view has led many churches to reject obeying God's Old Testament laws as being strictly for the Jews and no longer valid.
Systematic theology attempts to logically categorize Bible truths (doctrines) and summarize God's revelations to humans. It seeks to offer a comprehensive statement of beliefs regarding what Scripture teaches in an organized manner.