Final answer:
Charlemagne's most notable achievements include his conquest of vast territories, reorganization of the Church and promotion of education, and his role in the establishment of the Holy Roman Empire.
Step-by-step explanation:
Charlemagne, also known as Charles the Great, had several notable achievements. Firstly, he conquered vast territories across central Europe, uniting western Europe for the first time since the collapse of Roman authority. His empire extended from modern France to Germany, northern Italy, and parts of northern Spain and central Europe. Secondly, he reorganized the Church, establishing a strict hierarchy and promoting education and the creation of libraries. This period of intellectual and cultural revival is known as the Carolingian Renaissance. Lastly, Charlemagne played a significant role in the establishment of the Holy Roman Empire, a state that lasted for almost 1,000 years and had a major influence on medieval Europe.