This thesis describes the possibilities offered by the system Moodle in the assessment of students' achievement in teaching mathematics and computer science. Moodle is a very interactive platform for teaching, learning and evaluating students' achievement. In addition to being a free distance learning tool, it is widely accepted around the world, provides support for using the system, offers a lot of different options in the areas of user administration, courses, communication, collaboration and knowledge assessment. All a person needs to use Moodle is a computer and an internet connection. The Moodle system was created in 2002 with the aim of assisting teachers in creating virtual courses with an emphasis on interaction and collaborative content building. It can be used for teaching in classroom or for distance learning. In addition to creating virtual courses, teachers can use a system to evaluate students' achievements. The main part of the thesis is dedicated to the study of activities and modules offered by the Moodle system for assessment and tracking progress of students' achievements in mathematics and computer science. The activities and modules offered by the Moodle system can be used for formative assessment. Modules such as completion of activities and courses offer the possibility for students to track the completion of activities or their progress through the course, also the teacher in addition to tracking student progress may require students to meet a certain criteria before moving next in the course content. Moodle offers a variety of activities such as assignments, workshops, quizzes, games and more. With them, teachers can increase the student's motivation to learn. The assessment of educational outcomes is of great importance for students as participants in the educational process because it provides them with feedback on the level of knowledge obtained and the development of certain skills. The emphasis of using Moodle should be to encourage the student's self-tracking, self-assessment and taking control of their own learning. Teachers should use the Moodle system so that the student learns in a more interactive and interesting way for himself and his knowledge, not for a grade.