This book is based on a graduate course taught at the University of Paris. The authors aim to treat the basic theory of representations of finite groups of Lie type, such as linear, unitary, orthogonal and symplectic groups. They emphasise the Curtis-Alvis duality map and Mackey's theorem and the results that can be deduced from it. They also discuss Deligne-Lusztig induction. This will be the first elementary treatment of this material in book form and will be welcomed by beginning graduate students in algebra.