Written by one of the first Christian disciples, the Gospel of Luke is an account of Jesus Christ’s coming, birth, ministry and death. As a doctor (Colossians 4:14), Luke provided more focus on the miracles of healing that Jesus performed than his fellow Gospel writers, showing both his own keen interest in these things, as well as documenting them for future generations of Christian disciples. 1
Luke was not one of the twelve Apostles, but worked with Paul as a missionary, setting a fine example for Christians today. The overall theme of the Gospel of Luke is the Kingdom of God and the importance of that in the evangelising work that Jesus encouraged his Apostles and disciples to do – that they were to ‘…go and proclaim the Kingdom of God’. Jesus’ followers did exactly that - they ‘set out and went from village to village, preaching the gospel and healing people everywhere.’ (Luke 9:2,6,60; 10:1,9,11)2
The purpose of documenting miracles is to show all those who believe, what Jesus Christ is more than capable of achieving under His Kingdom. Out of all the miracles performed by Jesus, six are unique to the Gospel of Luke, and all serve to emphasise particular aspects of the Kingdom of God.3
• The provision of plenty is illustrated in the miraculous catch of fish in Luke chapter five:
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When he finished speaking, he said to Simon, “Put into deep water, and let down the nets for a catch.”
Simon answered, “Master, we’ve worked hard all night and haven’t caught anything. But because you say so, I will let down the nets.”
When they had done so, they caught such a large number of fish that their nets began to break… (Luke 5:4-6)
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• Jesus Christ’s command over death and his ability to raise the dead (as well as his compassion for mortal man), thus providing hope for humankind, is shown in Luke chapter seven:6
As he approached the town gate, a dead person was being carried out – the only son of his mother, and she was a widow. And a large crowd from the town was with her. When the Lord saw her, his heart went to her and he said, “Don’t cry.”
Then he went up and touched the coffin, and those carrying it stood still. He said, “Young man, I say to you, get up!”
The dead man sat up and began to talk, and Jesus gave him back to his mother. (Luke 7:12-15)7
• Jesus Christ’s willingness to heal affliction irrespective of a person’s age, gender or social standing, is shown in the three accounts found in Luke chapters 13, 14 and 17:8
- A woman bent double (Luke 13:11-13)
- A man suffering from dropsy (Luke 14:2-4)
- Ten lepers (Luke 17:12-14)9
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• Christ’s grace to everyone, despite their apparent loyalties, as shown in His restoring the ear of the high priest’s servant, which had been struck off by one of his Apostles. (Luke 22:51)11
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The Gospel of Luke is also the sole source of two well-known parables (as well as another seven that are unique to the Gospel of Luke):13
• The Good Samaritan (Luke 10:29-37), which is an important lesson for true Christians as to what ‘love thy neighbour’ really encompasses. Luke illustrated here that ‘neighbourly love’ meant not just saying, but demonstrating through actions that a Christian ‘loves’ their neighbour. This type of compassion, as shown by the Samaritan, should likewise be shown by Christians as they preach the Gospel of the Kingdom – tending for those Christian evangelize to in both the spiritual and physical senses.14
• The Prodigal Son (Luke 15:11-32). Above all things, this illustrates the Lord’s power of forgiveness – and the Grace He extends to all sinful Christians. It serves to show that irrespective of how far a person wanders from God, as long as he returns and is repentant, the Lord not only forgives him, but still promises him his inheritance – for Christians, the Kingdom of God.15
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As with the other Gospels, Luke also shows how Old Testament prophecy is fulfilled, therefore reinforcing the divinity of Christ and building a Christian’s confidence in the word of God, as well as strengthening his faith in the promises made by Jesus Christ in the course of His ministry. Luke also emphasizes the power of prayer, especially as regards providing strength for those who do the will of God. 17
Overall, the Gospel of Luke gives warmth and life to Jesus’ teaching. It needs no interpretation to illustrate His love, kindness, compassion and mercy towards the those afflicted by the human condition – especially as it gives a perfect example for Christian disciples to follow today in their own evangelizing work.18
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Adding your comment:
A good summery methinks. I can't think of anything I'd add. Though, Luke is, as far as I can tell, a lot more ordered than the other gospels, and due to the way it's written I don't think it shows quite as much of Jesus' love as John does. But then, that is what John was focused on when he wrote his book, Luke was more on the facts. From what I can gather (mention is made to his research in the start of Acts). 
