I am grateful to Luc Segoufin who kindly accepted me to be his PhD student. He introduced me to the problem of query enumeration and encouraged me to look for the answers to all the questions that emerged during our collaboration. He was a truly great advisor, always supportive and available for discussions and advice. I would like to thank Arnaud Durand and Patrice Ossona de Mendez for accepting to review this thesis and for their constructive comments on the earlier versions of this manuscript. Many thanks to Nicole Bidoit and Victor Vianu for accepting to be in my jury. Special thanks go to my Parents, who directed me to follow the scientific path and where fully supportive at all times. Thanks to all the members of LSV – it was a pleasure working with You. I would like to thank the awesome people whom I have been working with in the same office on the 4th floor. Without all the nice riddles and the magnificent French lessons my time there wouldn’t be as chouette as it was. Big thanks go to my son Boris, who was kind enough to sleep through the whole nights, allowing his dad to actually write the thesis down.