Human movement analysis is critical to optimizing sports training and influencing exercise intensity and effectiveness. In the age of modern technology, more and more advanced systems are emerging to support coaches and expand the range of analysis performed. This article aims to verify that artificial intelligence, together with machine learning algorithms, can accurately classify exercises in a dynamic gym environment and effectively assess the correctness of their performance. For the initial analysis of movement, the Google MediaPipe Pose model was used, which was responsible for detecting the human silhouette and determining the coordinates of the position of critical joints. Based on these coordinates, the angles between each joint were calculated, and then their sequences were further analyzed. The sequences were analyzed using the following three algorithms: support vector machine (SVM), dense neural network, and LSTM recurrent network. As a result, the system based on recurrent LSTM networks achieved the best prediction efficiency of approximately 98%, enabling accurate exercise classification. Subsequently, verification of the activities' correctness was also carried out, and the system, based on recursive LSTM networks, again achieved the best efficiency, this time equal to 96% on average for all exercises. On this basis, it was concluded that the discussed approach enables practical analysis of human movement, which can significantly improve training methods and facilitate coaching work.