The ancient civilization known for developing a complex calendar system is the Maya civilization. The Maya created a sophisticated calendar system that included multiple calendars, most notably the Tzolk'in (a 260-day ritual calendar) and the Haab' (a 365-day solar calendar). Their calendar was based on astronomical observations, enabling them to track celestial events and agricultural cycles with remarkable precision. The Maya calendar is notable for its mathematical sophistication and its ability to predict celestial occurrences, which held significant cultural and religious importance within their society. This advanced calendrical knowledge continues to be studied and admired today.