Counting systems are methods used to represent numbers and perform calculations. The most common system is the decimal system, which uses ten digits (0-9) to count and perform arithmetic. Other systems include the binary system, which uses only two digits (0 and 1), and is essential in computer science, and the hexadecimal system, which uses sixteen symbols (0-9 and A-F) to simplify binary representation. Different cultures have developed unique counting systems as well. For example, the Mayan civilization used a vigesimal system based on twenty, while the Roman numeral system employs letters to signify values. Understanding these systems helps us appreciate the diversity of mathematical concepts across the world.