Romans Summary of the studies in chapters 1-3 

Chapter 12v1-2 Therefore I urge you in view of God’s mercy, to offer your bodies as living sacrifices, holy and pleasing to God-this is your spiritual act of worship. Do not conform any longer to the pattern of this world but be transformed by the renewing of your mind. Then you will be able to test and approve what God’s will is – his good, pleasing and perfect will
FF Bruce quote: There is no saying what may happen when ordinary people begin to study the book of Romans

We are about to do our third study in the book of Romans. It’s a theological book with the word God coming up more times per verse than any other NT book but the aim of our studies together is not just to learn theology but to have our minds and lives transformed (see above quotes).
Paul starts (chap 1 v16 and 17) by saying how he is not ashamed of the gospel of for it is the power of God for the salvation of all who believe and he reveals a new insight: a righteousness of God, revealed through faith.  There then follows nearly 2  chapters of description of the failure and descent of man into wickedness and evil  starting by ignoring the evidence of our eyes (creation) and our hearts (conscience) and deciding to set our hearts on created things (wealth, people, career: idols) rather than the Creator Himself. Through this description of evil in1 v18 to 3 v20, Paul challenges us not to judge others because we all have the same problem (chap 2 v1 and 3 v27): all have sinned and fall short of the glory of God.

BUT NOW (chap3 v21) – these famous 2 words offer an escape from the downward spiral of wickedness and sin as Paul returns to the idea in 1v17 – a righteousness from God, through faith in Jesus and explains what it means in what some of called the most important paragraph ever written: 3v21-26.
In it he lists some very big theological words: justification, redemption (like a ransom being paid to rescue a slave), grace, atonement, propitiation (a controversial word because it means appeasing the wrath of God, see links below).

Justification. This means being declared innocent by God but its much more than that.  A judge might declare someone not guilty and say ‘you are free to go.’ What God does in justifying us freely is treat us like his own Son – not, you are free to go but you are free to come and enjoy a relationship with me.
Some of these ideas have caused debate and controversy even within the evangelical church on recent years, particularly around the wrath of God (Steve Chalke challenged the idea of propitiation,  that God’s anger had to be appeased by the death of an innocent in our place)and justification by faith (John Piper and NT Wright, 2 great evangelical Bible teachers of our generation have had a big debate about what this means).

Please see some links below if you interested in these ideas.