This paper aims to analyze the causes of flight delays of a selected airline operating in Europe and identify potential risks and reasons for delays in air transport, which carry risk, especially in connection with passenger dissatisfaction and the resulting need to pay compensation for delayed flights, according to EU law, which brings significant financial costs for airlines. Data collected from the years 2013–2019 have been used for the purposes of this article, including data on the duration and causes of the delays and the characteristics of individual flights, such as the flight type, aircraft type, time of departure, aircraft capacity, and the load factor. Multidimensional statistics methods have been applied for data processing, namely tests of independence and correspondence analysis. Dependencies have been presented in graphical form using correspondence maps. The analysis shows that the total share of delayed flights of the company in question does not increase over the mentioned period of time. The analysis furthermore proved that higher capacity aircraft were rather prone to longer delays. The share of delayed charter flights declined slightly over the period under review, while the number of delays caused by airline operating reasons, aircraft clearance by supplier companies, technical maintenance and aircraft defects, operating procedures, and crew flight standards and airport restrictions is increasing. The analysis also shows that the delays propagated by the delays of the previous flights are becoming more frequent, with the exception of the year 2019. In the last pre-COVID year, air traffic control could boast about a positive trend regarding the number of produced delays over the years, contributing to greater air passenger satisfaction and airline service quality. Due to the gradual revival of air transport after the COVID pandemic lockdowns, the topic of flight delays, passenger customer satisfaction and financial costs for the resulting delays is once again an actual issue for air management and operation.