There are two different genealogies given for Jesus: one in the Gospel of Matthew (1:1-17) and the other in the Gospel of Luke (3: 23-28). They are similar, of course, and in many aspects they're identical. At the same time, the differences between the two are important.
They remind me, in fact, of the two versions of Creation we find in the opening chapters of the Book of Genesis. In one version, the creative process moves from the very basic—sky, water, land—and culminates in the sixth-day creation of mankind. In the other, the creative process begins with mankind, after which everything else is created to serve and delight.
Likewise, the Matthew genealogy begins with Abraham, the first patriarch of Hebrew history and works forward in three 14-generation increments to the birth of Jesus. Luke describes the same genealogy in the opposite direction, moving backward from Jesus to Adam and then beyond Adam to God, the Source of All.
This makes sense because Matthew is "the Jewish gospel" written to affirm Jesus as the Messiah promised in Hebrew scripture. Luke was not Jewish himself, and his gospel emphasizes Jesus as a universally true and important spiritual teacher whose message was not meant to be for Jews alone. This combination of universal spiritual principle and its importance on our individual spiritual paths remains important for us today if we are to fully grasp the depth and breadth of the ministry of Jesus.