I agree with the two answers above but would like to add another important contribution.
Since with the fall of Roman and subsequent destruction, much of the ancient knowledge was destroyed. The Byzantine Empire, however, preserved and added to the existing mathematical and scientific knowledge.
For example in the field of mathematics, they took the Greek knowledge and added to it the mathematical knowledge from India and developed what today we call the Arabic numbering system which added two concepts missing form the more clumsy Roman sytem, place value digits and zero.
Their medical knowledge was superior to the crude Medieval system since the ancient medical knowledge, which was extremely advanced, was preserved and expanded upon.
As for architecture, the earlier European churches were thick walled. This was necessary since they did not have the mathematical knowledge of how to construct an arch. Once this knowledge became available, the graceful and beautiful cathedrals of the late Middle Ages and Renaissance became possible.
Despite the fact that the crusades were manufactured to determine which pope, the one in Rome or the one in Avignon, would be the supreme ruler of the church, and despite the fact that they failed to secure the Holy Land for the Catholic Church, the Crusades succeeded in ways unforseen by those involved.