At first I mostly followed the lecture structure of the previous professor, but over the years I streamlined it a lot, emphasized a "motivated" approach to each topic (e.g. "last chapter we did this, now we try to do this thing, it doesn't quite work, how can we fix it?"), and generally refined and simplified the explanations of everything. Teaching the same material year after year was a fantastic opportunity to identify the recurring sticking points and finding ways around them.