This book grew out of our fascination with the contraction-free sequent calculi. The first part, Chapters 1 to 4, is an introduction to intuitionistic and classical predicate logic as based on such calculi. The second part, Chapters 5 to 8, mainly presents work of our own that exploits the control over proofs made possible by the contraction-free calculi.

The first of the authors got her initial training in structural proof theory in a course given by Prof. Anne Troelstra in Amsterdam in 1992. The second author studied logic in the seventies, when by surprise Dag Prawitz mailed a copy of his book Natural Deduction. We thank them both for these intellectual stimuli, brought to fruition by the second author with a considerable delay. Since 1997, collaboration of the first author with Roy Dyckhoff has led us to the forefront of research in sequent calculi.

Dirk van Dalen, Roy Dyckhoff, and Glenn Shafer read all or most of a first version of the text. Other colleagues have commented on the manuscript or papers and talks on which part of the book builds, including Felix Joachimski, Petri Maenpää, Per Martin-Löf, Ralph Matthes, Grigori Mints, Enrico Moriconi, Dag Prawitz, Anne Troelstra, Sergei Tupailo, René Vestergaard, and students from our courses, Raul Hakli in particular; we thank them all.

Aarne Ranta joined our book project in the spring of 1999, implementing in a short time a proof editor for sequent calculus. He also wrote an appendix describing the proof editor.