Thus begins the book of Luke. Chapter 1 gives us details about John the Baptist, which is (apparently) intended to allow parallels between John and Jesus to be drawn for the readers. There may have been a motive for this, possibly the audience for this was mainly followers of John, so drawing parallels to Jesus might have been just the grease to smooth the transition to this new, improved prophet. I'm just speculating.
1 Forasmuch as many have taken in hand to set forth in order a declaration of those things which are most surely believed among us,
2 Even as they delivered them unto us, which from the beginning were eyewitnesses, and ministers of the word;
3 It seemed good to me also, having had perfect understanding of all things from the very first, to write unto thee in order, most excellent Theophilus,
4 That thou mightest know the certainty of those things, wherein thou hast been instructed.
Notice that the gospel is addressed to “most excellent Theophilus” but who Theophilus might have been remains a mystery. Here’s a site that ponders this fact. And, as always, here’s Wikipedia’s take.
Anyway - Chapter 1 is a looonnnggg one - by Bible standards - and traces John’s parent’s relationship with Mary and Joseph, through the conception of Jesus. We saw none of this in Matthew or Mark.
Chapter 2 presents us with material that we didn't see in Mark, and some that mostly - but not all - appears in Matthew. Here we get the truly lovely verbiage that we’ve all heard around Christmas time, and which probably formed my childhood understanding of Jesus:
There is also His circumcision, childhood in Nazareth, and boyhood hijinks in the Temple
7 And she brought forth her firstborn son, and wrapped him in swaddling clothes, and laid him in a manger; because there was no room for them in the inn.
8 And there were in the same country shepherds abiding in the field, keeping watch over their flock by night.
9 And, lo, the angel of the Lord came upon them, and the glory of the Lord shone round about them: and they were sore afraid.
10 And the angel said unto them, Fear not: for, behold, I bring you good tidings of great joy, which shall be to all people.
11 For unto you is born this day in the city of David a Saviour, which is Christ the Lord.
12 And this [shall be] a sign unto you; Ye shall find the babe wrapped in swaddling clothes, lying in a manger.
13 And suddenly there was with the angel a multitude of the heavenly host praising God, and saying,
14 Glory to God in the highest, and on earth peace, good will toward men.
15 And it came to pass, as the angels were gone away from them into heaven, the shepherds said one to another, Let us now go even unto Bethlehem, and see this thing which is come to pass, which the Lord hath made known unto us.
16 And they came with haste, and found Mary, and Joseph, and the babe lying in a manger.
Clearly he was growing up to be special!
43 And when they had fulfilled the days, as they returned, the child Jesus tarried behind in Jerusalem; and Joseph and his mother knew not [of it].
44 But they, supposing him to have been in the company, went a day's journey; and they sought him among [their] kinsfolk and acquaintance.
45 And when they found him not, they turned back again to Jerusalem, seeking him.
46 And it came to pass, that after three days they found him in the temple, sitting in the midst of the doctors, both hearing them, and asking them questions.
47 And all that heard him were astonished at his understanding and answers.
Chapter 3 is largely John the Baptist, Jesus’ baptism, John’s capture, and some (always) boring geneological stuff.
Chapter 4 finds Jesus being tempted in the wilderness
He perseveres, returns to Galilee to preach, then
1 And Jesus being full of the Holy Ghost returned from Jordan, and was led by the Spirit into the wilderness,
2 Being forty days tempted of the devil. And in those days he did eat nothing: and when they were ended, he afterward hungered.
...is presented with a sign that he is special - something I don’t think we’ve seen at this early stage of his ministry. We also see that some of the passages are getting out-of-order, when looked at from Luke’s perspective back to Mark and Matthew. It’s not prevalent, but enough to - again - catch the eye of the inquisitive.
16 And he came to Nazareth, where he had been brought up: and, as his custom was, he went into the synagogue on the sabbath day, and stood up for to read.
17 And there was delivered unto him the book of the prophet Esaias. And when he had opened the book, he found the place where it was written,
18 The Spirit of the Lord [is] upon me, because he hath anointed me to preach the gospel to the poor; he hath sent me to heal the brokenhearted, to preach deliverance to the captives, and recovering of sight to the blind, to set at liberty them that are bruised,
As I already mentioned, Luke adds new material that is missing from Mark, and partially missing from Matthew. I think the weaving together of John the Baptist’s and Jesus’ stories is most significant, as well as is the lovely images given to us by the birth and adoration narrative. Have a look at Gospel Parallels, if you feel the need to get more in-depth.