According to the standard Synoptic Gospel theory Luke was written in the 80s or even 90s C.E. and incorporated the narrative of Mark, the sayings of Jesus in Q, and a large quantity of his own material (L). Remember that Luke-Acts is a two volume (scroll) work, with a formal preface, written for a patron, and based upon claims of research. The two books should not really be separated as they are now in the N. T. It reminds us of other Greco-Roman biographies and histories of the time. This is in contrast to Mark (dramatic mystery), and Matthew (teaching book).
You should give attention to:
Structure: how he weaves his material together
Style: how he edits and presents his sources and makes use of his own material
Content: what he eliminates or adds; what are his major concerns, themes, and emphases
Structure
Mark is generally followed and becomes the basic narrative structure of Luke
Note how the Q material is incorporated
Note the “great omission” of Mark 6:45-8:16 (see Luke 9:10-22!)
Note the “great insertion” that runs from 9:51-18:14 (see Mark 9:38-41 and 10:13-16)
Style
Review some good examples of Luke’s version of Q compared to Matthew’s
Find some good examples of how Luke edits his source Mark compared to how Matthew edits the same
What are the tendencies of Luke in carrying over his sources Mark and Q?
Content
What are the major themes and emphases of Luke?
Look for the themes that run through his special material
Note how he eliminates key or difficult passages in Mark (especially regarding the failure of the disciples)
Note what he adds to the Markan narrative that helps carry his overall presentation of the Gospel