what purpose do you think strobel wants to accomplish with this book?

The author is foremost an apologist for Christianity. While this is the title of the book, it is also Strobel's overall theme. The other themes, the "reliability of the gospels" and "evidence," are intrinsically tied in with the case for Christ, because the reliability of the gospels is based on evidence. It is this collection of evidence that proves the reality of Christ in his deity and humanity.