Are there books or lecture notes that comprehensively introduce the (geometric/topological) theory of mechanical linkages, as well as important results and their proofs? For instance, Kempe's Universality Theorem and its proofs.
I'm not looking for the robotics side of the theory, just the "pure mathematical" aspects such as configuration spaces.
Edit: I have already read Geometric Folding Algorithms: Linkages, Origami, Polyhedra by Erik D. Demaine. It is an excellent book but I would like to have as much background as possible so please recommend me more books, if there are any more good ones.
I recommend the book Geometric Folding Algorithms: Linkages, Origami, Polyhedra by Erik Demaine. It's commonly accepted as systematical introduction on Linkages theory from mathematical as well as algorithmic aspect aimed more at graduate students and researchers. You will find many surprising and amazing results came out easily from so simple and even direct from mathematical induction and deduction.
Addition: First time when I touched this field I read How to Fold It by J O'Rourke. But I think it, though readable, introduces only basic results with simple proof aimed at beginner.