I bought a book by Wayne Grudem called Systematic Theology: An Introduction to Biblical Doctrine. I'll make summaries and journal a path through this book (or at least try to anyway).

Systematic Theology

Definition - The study of what the bible as a whole has to say about any given topic today. It differs from historical theology, philosophical theology, apologetics, and biblical theology (because biblical theology includes a study of how those doctrines may have been understood over time and gives attention to individual authors and sections of scripture).

Luke 24:27 - Jesus opens the scriptures and explains to them systematically about Himself, the Messiah.
"And beginning at Moses and all the Prophets, He expounded to them in all the Scriptures the things concerning Himself."

Acts 18:28 - Apollos uses the scriptures to convince the Jews of Jesus.
"For he vigorously refuted the Jews publicly, showing from the Scriptures that Jesus is the Christ."

Acts 17:2-3 - Paul handles the scriptures systematically to prove that the account of Jesus was in prophecy.
"Then Paul, as his custom was, went in to them, and for three Sabbaths reasoned with them from the Scriptures, explaining and demonstrating that the Christ had to suffer and rise again from the dead, and saying, 'This Jesus whom I preach to you is the Christ.'"

Doctrine

A doctrine, then, is what the bible as a whole has to say about one particular topic. Therefore, the Doctrine of the Deity of Christ, The Doctrine of the Trinity, or the Doctrine of Salvation are all

Advantages to Systematic Theology

Because our time here is short, and we can't read the bible as a whole for each and every theological question, it's advantageous to have the specific passages on that particular question to examine ready. It's also apart of fulfilling the Great Commission of Matthe 28:19, '...make disciples, teaching them to observe all things whatsoever I have commanded you...' Jesus Christ embraced the Old Testament as the infallible revelation of God and the Holy Spirit supervised and authored the writing of the New Testament, giving us a clear basis to study God throughout the bible. It also overcomes bad ideas that we might have accumulated that sound scriptural, but aren't biblical, leading us to the truth the bible declares. Systematic Theology doesn't somehow 'improve' on the bible.