Reed-Solomon codes are cyclic linear block codes. They are used in various domains of digital communication and data storage. They are most commonly used in satellite communication, mobile and wireless communication, and storage devices (QR codes, barcodes, CDs, DVDs). This thesis describes the functionality of Reed-Solomon error correction codes. The error correction begins with converting information into a codeword using the Galois fields and their generator polynomial. After the message is transformed into a codeword, it is sent into the communication channel by the encoder. In order to get the message to the receiver, it has to go through a decoder. The process of correcting the codeword's errors is explained to the final step of finding the values of the errors and correcting the received codeword. The thesis provides examples related to the corresponding functionalities in order to contribute to a better understanding of the entire process of Reed-Solomon error correction codes. Hamming codes are shortly described, including the comparison with Reed-Solomon codes.